Grilled Chicken Salad with Corn, Peppers, and Tortilla Chips Recipe

2 boneless chicken breasts with the skin (about 1 1/2 pounds), halved
1/2 cup fresh lime juice
1 teaspoon dried orégano, crumbled
vegetable oil for brushing the chicken
4 corn tortillas, cut into long thin triangles
vegetable oil for frying the tortillas
2 cups cooked fresh corn kernels (cut from about 4 ears)
1 large red bell pepper, diced
3 scallions, sliced thin
2 tablespoons fresh lime juice, or to taste
1 tablespoon finely chopped fresh orégano or 1 teaspoon crumbled dried, or to taste
1/2 teaspoon ground cumin, or to taste
1/4 cup olive oil
1 bunch of arugula, washed well and spun dry

In a bowl let the chicken marinate in the lime juice with the orégano and salt and pepper to taste, covered and chilled, for at least 30 minutes or up to 1 hour. Drain the chicken, pat it dry, and brush it with the oil. Grill the chicken, seasoned with salt and pepper, on a well-oiled rack set about 6 inches over glowing coals for 6 to 7 minutes on each side, or until it is just cooked through. (Alternately, the chicken can be grilled on top of the stove in a ridged grill pan over moderately high heat for about the same length of time.) Transfer the chicken to a cutting board and let it stand for 10 minutes.
In a heavy skillet heat 1/2 inch oil to 375°F. on a deep-fat thermometer and in it fry the tortilla triangles in batches for 45 seconds to 1 minute, or until they are golden, transferring them with a slotted spatula as they are fried to paper towels to drain and sprinkling them with salt. The tortilla crisps may be made 1 day in advance and kept in an airtight container.
In a large bowl combine the corn, the bell pepper, and the scallions, add the lime juice, the orégano, the cumin, the oil, and salt and black pepper to taste, and toss the mixture until it is combined well. Cut the chicken lengthwise into thin slices and add it to the corn mixture with any juices that have accumulated on the cutting board. Divide the arugula and the tortilla crisps among 4 plates and mound the chicken salad in the center of each plate.