Warhammer 40,000: Dawn of War III is the possible future sequel to Dawn of War and Dawn of War II, expected to be developed by Relic Entertainment. It is not in production, and despite being confirmed earlier by THQ (the previous publisher) representative Danny Bilson, the announcement has been retracted since (see below).
According to the August 2010 statement by Bilson, Dawn of War III would have been expected 18–24 months after Dawn of War II: Retribution. This would have meant late 2012 to early 2013. However, THQ started having financial problems since, which led to layoffs at Relic followed by announcement of Company of Heroes 2 for 2013. Bilson later commented that the studio had to focus all resources on Company of Heroes 2 and that they are "doing some rethinking" regarding Dawn of War III. 
In December 2012, THQ filed for bankruptcy, and in January 2013 it was announced that Relic was being sold to Sega. It is not known if the development of Dawn of War III will continue under Sega; however, seeing as Sega recently acquired a license for developing a Warhammer Fantasy video game from Games Workshop, it seems realistic to expect they are looking to continue Relic's 40K franchises as well.
Since the game is not in production, nothing is known or set about it. It was suggested that Relic would go for a larger scale than Dawn of War II and that they might model it on Company of Heroes Online if the title proved successful (which it didn't, ending up closed in March 2011). Danny Bilson later indicated the studio being in "a bit of a rethinking mode" regarding Dawn of War III.
"There's a lot of rethinking going on right now with the RTS 40k stuff. We're going to do something different, but we're in a bit of a rethinking mode. [...] we're doing some rethinking. What that really has to do with is the RTS business, and what's the best way to present RTS? We're not getting out of RTS. It's just, what's the best way to present it in the future? We'll be talking more about that later." 
Plans for Dawn of War III were claimed by Danny Bilson (Executive Vice President, Core Games, THQ) to Eurogamer in an interview on August 18, 2010.
As part of Gamescom 2010 yesterday, THQ took the lid off of Warhammer 40,000: Dawn of War II - Retribution, the second full expansion to Relic's well-regarded sci-fi real-time strategy series. It now appears as if it will also be the last, as THQ core games vice president Danny Bilson told Eurogamer today that once Relic ships Retribution in February, the team will transition into working on Warhammer 40,000: Dawn of War III.
"Retribution's going to ship in February, and then we start laying out Dawn of War III," Bilson said. "You can probably expect it between 18 months and two years after that." Following Bilson's timeline, Dawn of War III's release date would fall into the August 2012 to February 2013 window.
What's more, THQ may consider to adopt the same business model it is using for Relic's Company of Heroes Online with Dawn of War III. Having successfully launched a free-to-play, microtransaction-supported version of Company of Heroes in Asia in 2007, THQ said in June that it would be bringing the same free-to-play game to Western audiences this fall.
"It may be a more digital free-to-play experience with all the depth and quality of a Relic RTS," Bilson stated, before going on to note that Dawn of War III's free-to-play status hinges upon the success of Company of Heroes Online.
"It all depends on how COHO does, and how it works and how people respond to it," he continued. "If they do that would definitely drive us to… Now Dawn of War III, either way, is going to have a much larger strategic component to it, more of a global battle going on with little tactical things, sort of MMO-like…We haven't announced anything about it, and it's still in its early formative stage, but I'm just talking to you about the brainstorming going on around it." 
A Relic Entertainment marketing manager, James McDermott, gave further details on Relic's Dawn of War III plans in a further July 2011 interview to Eurogamer:
Upcoming real-time strategy game Dawn of War III will allow gamers to build their own custom armies, developer Relic has revealed. It will also simulate the idea of a "war that rages eternal," Relic marketing manager James McDermott told Eurogamer.
"Looking at what we had real success with with Dawn of War II – Retribution, with the DLC, and with customisation and building their armies and collecting being a big part of what 40k fans really love, we want to make that a big part of DOW3," he said. "There's going to be lots of opportunities to expand and build your own custom mega army. That's definitely an area we want to invest in. We see a good opportunity."
Last year Eurogamer broke the news that Relic was in the brainstorming stage of Dawn of War III. THQ core games boss Danny Bilson suggested the Warhammer 40K RTS would launch between 18 months and two years after Dawn of War II - Retribution, pegging DOW3 for an August 2012 to February 2013 release window. He also said the game "is going to have a much larger strategic component to it, more of a global battle going on with little tactical things, sort of MMO-like".
Now more gameplay details have trickled out ahead of what THQ has teased will be an announcement at German show Gamescom next month. With Dawn of War II, Relic dropped base building – although it did feature in a reduced way in the game's multiplayer.
"We brought some base building back with Retribution," McDermott continued. "With DOW3, because it's going to be a new version, we're looking at the game as a whole, and we're really upping the intensity. With the 40k universe, the tagline is: there is only war. We want to give you that greater sense of the war. The battle. The war that rages eternal, and make that feel like that's really imposing and all around you, and you have your own personal, custom army in there. Your army and my army should feel very different. That's where we would like to get to.
"We're trying to leverage even more so on the Games Workshop tabletop game, and then combine that with the game mechanics people have said, 'If you were to make a DOW3 we would like this kind of balance of things,' and what we think would be good for strategy games as a whole. We're looking at all that stuff really carefully. And I'm sure you've probably heard this as well about Relic – we have a big announcement at Gamescom."
Is it Dawn of War III? Or perhaps Company of Heroes 2, the sequel to Relic's excellent World War II RTS?
"There is something cool and I think people will be really pleased to hear about it." 
Danny Bilson (Executive Vice President, Core Games, THQ) commented present Dawn of War III plans to Eurogamer in an interview published on May 30, 2012:
Eurogamer: I have to ask about Dawn of War 3, which you've spoken to Eurogamer about before. You mentioned an announcement that didn't materialise. What's happening with it?
Danny Bilson: There's a lot of rethinking going on right now with the RTS 40k stuff. We're going to do something different, but we're in a bit of a rethinking mode. What we had to do at Relic was prioritise Company of Heroes 2 now and then move back to 40k. With that we moved that over here for a bit - just a bit - because we needed to load all the resource onto making Company of Heroes 2 awesome.
But look, everybody at Relic loves 40k. I love 40k. I also have tremendous respect for Games Workshop and the people I work with there. They're some of the best people I've ever worked with in my career. So I personally feel really strongly about that brand.
Eurogamer: So Dawn of War 3 isn't dead?
Danny Bilson: No. But we're doing some rethinking. What that really has to do with is the RTS business, and what's the best way to present RTS? We're not getting out of RTS. It's just, what's the best way to present it in the future? We'll be talking more about that later. There are aspects of Company of Heroes we haven't talked about that are progressive and forward thinking, that we'll roll out between now and the launch of the game. We're just giving you the first look at Company of Heroes 2. There's actually more to it.