We have seen the duck and goose grab a chicken when it was drinking from their pond (which is really a big rubbermaid tank about 2 1/2 feet by 4 feet). We have also seen the duck try to mate with chickens by grabbing them by the neck. We found the chicken dead in the pond with blood on it's head, beak, and neck. They might have actually broken it's neck rather than drowned it but (being a little squeamish) I didn't check it that close when I pulled it out of the water. We do have a goose and gander who have been playing at mating but don't think they've really done anything yet. Our poor little drake is in line to get some females this spring, but he doesn't have any yet. The goose and gander get upset even when the chickens lay eggs and make noise. They don't like the chickens drinking from their water or eating from their food dish (or the greenhouse, hehe) and run them off by biting at them or grabbing them by the neck feathers. Usually the chickens avoid the geese and do their own thing.
We haven't had any problems with it since we added another two feet of netting to the top of the chicken yard enclosure. As long as the chickens can't start flying higher than the 8 foot fence, we're good I think. Never know with animals about though ...