In a large pot of boiling water, cook beans until crisp-tender, about 3 minutes. Add bell pepper, and stir to submerge. Using a small sieve, transfer vegetables to a bowl. Add noodles to boiling water, and cook until al dente according to package directions, 4 to 6 minutes. Drain, rinse thoroughly with cold water, and reserve.
Meanwhile, in a small skillet, bring 1 cup salted water to a simmer over medium heat. Add chicken breasts; cover, and cook 5 minutes. Turn off heat; let steam until chicken is cooked through, 5 to 10 minutes. When cool enough to handle, shred chicken with a fork.
In a large bowl, whisk together lime juice, soy sauce, and sugar. Add reserved vegetables and noodles, chicken, pineapple, mint, and 1/4 cup peanuts; season with salt and pepper. Toss to coat with dressing. Serve immediately, topped with remaining 1/4 cup peanuts.
Also, this salad can be prepared up to a day ahead of time and refrigerated in a covered container, but the pineapple should be added just before serving.
Angel-hair pasta can be substituted for the rice noodles in this recipe. To save time, you can use store-bought roasted chicken, and skip step two.