Heat the olive oil in a frying pan over medium heat. Cook and stir the onion until tender, and quickly brown the chicken on all sides. Remove from frying pan, and set aside.
Place the ground walnuts in the remaining oil in the frying pan. Over medium heat, cook and stir 5 to 10 minutes, until lightly browned.
Return the onion and chicken to the frying pan with the walnuts, and blend in the pomegranate syrup. Reduce heat to low, cover, and simmer 20 minutes, stirring occasionally, until chicken is no longer pink and juices run clear.