"teleports the chicken at the coordinates of the player, but not 10 blocks away."
Dear Kumasasa, with the command you used it is indeed not possible to teleport a chickn 10 block from the player. Though this should be possible with the execute command in the way charlie proposed it (although it should be tp instead of /tp since you already used the slash in /execute, but neither of both work). I tried it to and i can confirm it doesnt work. I would ask to reopen this thread since this is a bug.
Sorry, has already been reported, couldn't find it before I placed it though.