For the marinade, in a medium bowl whisk together lemon juice, shallot, mustard, and the 1/4 teaspoon salt. Gradually add olive oil, whisking until combined; cover and set aside.
For the chicken, place each chicken breast half between two pieces of plastic wrap. Using the flat side of a meat mallet pound chicken lightly until 1/4-inch thickness. Discard plastic wrap. Place chicken in a large resealable plastic bag set in a shallow dish. Add marinade. Seal bag; turn to coat chicken. Marinate in the refrigerator for 30 minutes to 3 hours.
Drain chicken, discarding marinade. Season with salt and pepper. For a gas or charcoal grill, grill chicken on the greased rack of an covered grill directly over medium coals for 4 minutes or until no longer pink, turning once halfway through grilling.
To serve, place chicken on four serving plates and top with Gazpacho Salsa.