Oh absolutely. I've seen a crow fly off with an egg in it's mouth. In our case, they normally take the eggs out of the house which I know can't be done by a chicken (we do have a egg pecking chicken too). Very little you can do about it although I have found having a broody hen in the house helps - she gathers them under her and I collect them from her once a day. Beyond that we have tried everything to get rid of the crows - we have about 50 or 60 that fly down every morning after I put the food out. Even a man with a gun only keeps them off whilst he's actually there - which is about as effective as a real-life scarecrow. The minute they see him walk off, they're back down. I think ours will go once harvest happens because there's really not that much food up in the run now (I limit what I put out in the morning to what my birds can eat pretty rapidly and then feed them again last thing in the evening after the crows have gone to roost and just before they go into the sheds) so once there's corn in the fields, I hope they'll be off. Meantime, complete nightmare!