The foxes in Minecraft will chase any chicken they see, even if the chicken in question is above deep water. Now foxes can float a bit on the surface of water, but if they jump at the chicken they'll get stuck under the surface of the water, slowly float down to the bottom and start drowning. Every other minecraft animal I've seen so far was able to swim back up to the surface, so I thought it was odd see that the foxes didn't.
I've tested it, and it seems that foxes that jump down into the water and get further than 5 blocks deep won't be able to swim back up by themselves. However, foxes that are spawned on that depth do swim up, as do foxes that don't dive deeper than 4 blocks.