Put a large pot of water on to boil for cooking pasta. Meanwhile,place chicken in a skillet or saucepan and add enough water to cover. Bring to a boil. Cover. Reduce heat to low and simmer gently until cooked through and no longer pink in the middle,10 to 12 minutes.
Transfer the chicken to a cutting board. When cool enough to handle, shred into bite-size strips. Whisk peanut butter,soy sauce,garlic, chile-garlic sauce and ginger in a large bowl.
Cook pasta in the boiling water until not quite tender,about 1 minute less than specified in the package directions. Add vegetables and cook until the pasta and vegetables are just tender,1 minute more. Drain, reserving 1 cup of the cooking liquid.
Rinse the pasta and vegetables with cool water to refresh. Stir the reserved cooking liquid into the peanut sauce. Add the pasta, vegetables and chicken. Toss well to coat. Serve warm or chilled.Cover and refrigerate for up to 2 days. Serve cold or reheat in microwave.