If the turtle was out of water, it was likely going to lay eggs, as this is the season for such an activity. Outside of the water is the only time a large animal has any reason to be wary of a snapper. In water they are docile and will try to get away from you or ignore you rather than bite. I've found many a snapper in the mud of ponds by locating their shell and orienting myself by feeling around and finding their head, and I've never been bitten by a snapper in water.
As far as your chickens go, large snappers will take fowl, but they eat relatively little for their impressive size and are likely not the culprit you are looking for. An adult snapper large enough to take a chicken would also be at a point in it's life where even if this was it's only food source it would take very few of them a year. Even moving this animal you will probably find that your chickens will continue to disappear. After it is moved, or before, make a careful check of your arrangements for the fowl and see that they cannot be taken by skunk, possum, fox, coyote, eagle, hawk, dog, cat, raccoon, etc.
There's a post on here about turtle traps. In your case you'll need to make a very large one to handle it, but the design should work fine if you find sturdy enough materials.