Place the chicken in a large saucepan of water and bring to a boil over moderate heat.
Reduce the heat to low and simmer, uncovered, until no longer pink on the inside about 10 minutes.
Meanwhile, cook the linguine according to package directions.
Whirl the peanut butter, water, soy sauce, vinegar, sugar, and oil in a food processor or electric blender at high speed for about 30 seconds or until smooth, then transfer to a large bowl.
Drain the chicken breasts and let cool on paper toweling.
Drain the linguine, rinse well, and add to the bowl with the peanut mixture.
Using your fingers, pull the chicken into long, thin shreds and add to the bowl along with the cabbage and sliced scallions.
Toss well to mix, then sprinkle, if you like, with the chopped scallion and peanuts.