Please don't burn them. They will put huge amounts of air pollution--even burning clean, dry seasoned firewood puts out tons of air pollution including toxics and particulate matter. Shavings will also throw up mold spores and other goodies. Also, it might not be legal in your state. Here in Ohio, it is not.
Since you say you don't have the space to keep them, have you thought about advertising them free for the taking on Craig's List or something similar? I have a really big garden, and the chicks don't provide enough poop for it. I find people with horses giving away poop on CL and go pick it up. Good for me, good for them.
p.s. I work for the Environmental Protection Agency here, so if you really want the litany of what nasty stuff burning wood throws into the air, let me know. Suffice it to say, it isn't the clean process people assume it to be.