Whether a bird has a beak or a bill depends upon its feeding habits. Birds that need to peck at the ground or at trees in order to find grain, fruit and insects have a hard, pointy beak. Birds such as waterfowl (ducks, geese) that catch small fish and other aquatic creatures have a longer, flatter bill (as opposed to a beak).
A chicken has a beak; in your sentence, "off of the ground" is fine, or you can say "from the ground."
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