Turn chair upside down. Clean lint and debri from underneath. Locate the opposing wood pieces on each side, that contact each other, when the chair makes its rocking motion. Tip chair side ways towards you so you can drip candle wax on the surfaces where those pieces make contact. You my as well use white lithium grease on any metal sliding parts while you are under there. That squeak was driving me crazy too. It is the wood against wood, after it has dried out.
Mark M., November 2010