Even though 'Chateau' literally translates as 'Castle', what it is usually applied to is more an (unfortified) country house than a castle. I think it more likely that they would become available with Architecture rather than Chivalry.
I have the suspicion that Chateau spamming is going to be prevented by not allowing two of them to be build adjacent to each other, which historically makes sense as it was the residence of a major landowner. If you look at the screenshot, you'll see that they aren't indeed next to each other, but also that there are undeveloped tiles next to some of the Chateau.