I asked the same question. This website explains in detail. But essentially, chickens can be carriers of blackhead disease which will kill turkeys. So no you can't keep them together.
These are my birds, so far I havent had any issues. Our bird pen has a variety, 4 turkeys, 1 RHR & 1 EE (i think) we all purchased close to the same time. they were just wee little pullets. They have been introduced to the outside pen with 2 runners, 4 hens and one roo every one gets along fine. The older ones only go to the coop to roost & lay. I'll keep you informed as they all grow.