Remove tenders from underside of each breast if present (save for another use). One at a time, place each breast, smooth side down, between 2 sheets of plastic wrap. Pound to even 1/2-inch thickness (see "pounding chicken," below).
In large resealable bag combine the 1/4 cup olive oil, 2 Tbsp. of the lime juice, the garlic, salt and pepper. Add chicken, press air out of bag, and seal. Turn to coat evenly. Marinate, refrigerated, for 1 to 2 hours.
Prepare grill for direct cooking over medium heat (about 400 degrees F). Prepare Tomato-Corn Salsa: Brush onion, tomatillos, corn, and chile with olive oil. Grill vegetables over direct medium heat, with lid closed as much as possible, until onions are lightly charred, tomatillos soften and begin to collapse, corn is tender, and chile is softened and lightly charred, turning as needed. (About 10 minutes for onion, and 12 to 15 minutes for tomatillos and chiles.) Place chile in bowl. Cover with plastic; let steam 10 minutes.
Peel off skin from chile; discard. Remove stem and seeds. Place vegetables (except corn), cilantro, brown sugar, and 1/4 tsp. salt in food processor or blender. Whirl until pureed; stir in corn. Add more brown sugar or salt to taste.
Increase grill temperature to high (about 500 degrees F) or add additional coals and heat until high heat is reached. Remove chicken from bag, letting excess liquid drip back into bag; discard liquid. Grill chicken, smooth side down, over direct high heat, with lid closed as much as possible, until well marked, 3 to 4 minutes. Turn; grill just until cooked all the way through, 1 to 2 minutes more. Transfer to a platter.
In bowl whisk together sour cream, the 1 Tbsp. olive oil, lime zest, remaining juice, 1/4 tsp. salt, and 1/4 tsp. pepper. To serve, spoon salsa over chicken. Pass lime sour cream, lime wedges, sliced jalapeños, and cilantro. Makes 6 servings.
Pounding Chicken: Jamie pounds his chicken, so that it cooks faster and more evenly. Place chicken breasts between two pieces of plastic wrap. Using a flat meat mallet or rolling pin, gently pound meat, starting at the thicker end of the breast and pounding to an even 1/2-inch thickness.
Direct Grilling: For this method, the food is placed on the grill rack directly over the heat source. Direct grilling is best for searing and cooking small, tender cut that cook in 30 minutes or less, such as steaks, burgers, or boneless chicken.