Left is
又 'again/hand' — a pictograph of a right hand. In
鸡 it serves as a simplified phonetic substitute. The traditional
雞 had
奚 on the left, a 10-stroke phonetic; the 1956 reform replaced it with the 2-stroke
又 to slash the character's complexity. The sound link to jī is loose — this is a reform-era shortcut where the radical does most of the work.