In a shallow dish, whisk together the lemon juice, vinegar, oil, stock, and garlic. Reserve 3 tablespoons. Add the chicken, turning to coat, and marinate for 20 minutes.
Meanwhile, prepare a stove-top griddle or outdoor grill. Grill the peppers, turning frequently, until charred and wrinkled, about 10 minutes. Remove to parchment paper to cool. Peel over the parchment paper, reserving the juices. Cut the peppers into 1/4-inch strips and place in a bowl. Stir in the collected juices and the reserved marinade. Season with salt and pepper.
Grill the chicken until the juices run clear when pricked at the thickest point, about 4 minutes per side. Arrange the chicken over the Caramelized Corn with Shallots and spoon the pepper mixture on top. Garnish with the basil.