You can certainly brood chicks anywhere. It's strictly accepted convention that we go get the requisite "box", fashion it into a brooder, and install baby chicks with a heat lamp focused on them.
Last year, after doing some critical thinking, I saw so many reasons why brooding this way is, well, stupid. Chicks really do not benefit from it in any truly significant way, and in so many more ways, brooding indoors in a "box" is detrimental to their development and well being.
After years if observing chicks during and after being brooded indoors in the conventional manner, I concluded that brooding them out in their coop or run is far better, and I listed all the reasons why. The article is linked below this post, the second one of four articles I've written for BYC.
So, by all means move your chicks out to the coop. Everyone will be much happier, including you.