From North:

Speedway A1 to Florence, then take Impruneta exit. Continue on the way to Siena then take Siena-North exit. Follow the signs to Castellina in Chianti.
 

From South:

Speedway A1 from Rome to Val di Chiana, then take Valdichiana exit. Continue on the Bettolle-Siena way then follow the signs to Florence. Take the Siena-North exit and follow the signs to Castellina in Chianti.