Stir-fry the chicken in oil until opaque and lightly browned, 2-3 minutes. Remove with a slotted spoon and set aside.
Bring the chicken broth to a boil in the same skillet, add beans, cook until the beans are tender-crisp. Stir in the green onions and water chestnuts.
Mix the vinegar, water, soy sauce and cornstarch until smooth. Return chicken to the skillet, add snow peas and the cornstarch mixture, cook just until heated through and slightly thickened, 2-3 minutes. The snow peas should be tender-crisp.
Serve over hot brown, or white, rice. Garnish with the reserved green onion tops and choice of nuts.