1. Preheat a grill or grill pan misted with cooking spray to medium high. Separate chicken tenders from breasts. Place chicken in a large resealable plastic bag; press air out of bag and seal. Pound chicken with the smooth side of a meat mallet or a rolling pin until about 1/2 inch thick. Remove chicken from bag and sprinkle both sides with 1/4 teaspoon salt.
2. Grill chicken until no longer pink in the center, 4 to 5 minutes a side on the grill or 5 to 7 minutes a side in a grill pan. Let rest 3 to 5 minutes before slicing into 1/2-inch-thick strips.
3. Meanwhile, whisk together vinegar, shallot, mustard and remaining salt in a small bowl. Whisk in oil and season with pepper. Arrange mixed greens, plums, goat cheese and chicken on a large platter. Drizzle dressing over salad.