In pot over boiling water, place green beans and cook about 5 minutes. Drain beans; run under cold, running water.
Place olive oil, lemon juice and cilantro into the bowl of a food processor. Whirl until cilantro is finely chopped. Remove 1/2 cup of olive oil marinade; place in a large zip lock plastic bag. Set aside.
Add walnuts, walnut oil, garlic, salt and pepper to other ingredients in the food processor. Whirl until walnuts are finely chopped; set aside. Place dressing in bowl; cover with plastic and refrigerate.
Place chicken thighs in zip lock bag with marinade; seal tightly and shake well. Refrigerate for at least 30 minutes and up to 24 hours.
Prepare coals for grill. When coals are hot, place chicken on grill and cook, turning often, for about 20 minutes. Just before serving, toss green beans with dressing. Arrange the beans on a platter and set cooked chicken on top.