Coarse salt and ground pepper
8 ounces soba (Japanese buckwheat noodles)
2 tablespoons vegetable oil, such as safflower
1 teaspoon toasted sesame oil
2 tablespoons fresh lime juice, plus lime wedges, for serving
2 tablespoons rice vinegar
2 bell peppers (ribs and seeds removed), thinly sliced
1 cup torn fresh basil leaves
1 English cucumber, peeled, halved lengthwise, seeded, and thinly sliced
1 rotisserie chicken, skin and bones removed, meat shredded (about 4 cups)