If there isn't someone standing guard over them with a weapon that can eliminate the threat farther than the chickens range I wouldn't turn them out. Especially if I saw tracks with only 3 prints & a hitch in the gait.
I agree with the majority. Time for the injured coyote t be put down. Hoodat is right. Better quick than slow. Around these parts coyote are considered Varmits. Open season year round, no limits. But the are not called willey coyote for no reason! DH and DS have tried often with no luck.