In a skillet, bring 1 cup salted water to a simmer. Add chicken, cover, and cook over low heat 5 minutes. Turn off heat; let steam 5 minutes. Shred chicken with a fork.
Cut lettuce and bell peppers into strips; slice scallions. Quarter cucumber lengthwise; slice thinly. Combine vegetables and chicken; season with salt.
Toss with peanut vinaigrette and peanuts.