1. Combine green beans and 1 cup lightly salted water in a microwave-safe bowl; cover. Microwave on high until beans are crisp-tender, about 4 minutes. Drain.
2. In a bowl, whisk 3 Tbsp. oil along with mustard, vinegar, 1/2 tsp. salt and shallot. Add green beans, tomatoes and white beans and toss to coat.
3. Preheat a gas grill to high. Brush chicken with remaining 1 Tbsp. oil; sprinkle with salt and pepper. Grill, covered, until chicken is cooked through, turning once, 8 to 10 minutes total. Let cool slightly; chop.
4. Add chicken to bowl and toss again. Serve.