Chickens often are carriers of Blackhead disease, and are immune to it. It's in their poo, and when the turkeys step on it, they can catch it. It's like an internal organism/parasite type thing that affects the liver. I researched first, by asking a farmer friend of mine who raised his chickens and turkeys together, and then I talked with two breeders who raised them together. I think there is number to call for information like that in your state regarding livestock, but I'm not sure what it's listed under.
I just researched Blackhead too, so that I know the symptoms, and I can take care of it if I see it, but my turkeys are 7 months old now and very healthy.
If you have the room, it would probably be best to keep them separated and be 100% safe, but for me, it's fine.