Season chicken with salt and pepper. Place in a shallow dish and spoon two-thirds of the lime juice over. Let sit 15 minutes. Meanwhile, julienne peppers and onion.
Prepare a stove top griddle or an outdoor grill. Remove chicken from lime juice; discard the juice. Grill chicken 5 minutes per side, or until juices run clear when pricked at the thickest point. Remove to a cutting board to cool. Meanwhile, warm tortillas on the grill, turning frequently until they begin to puff slightly, about 1 minute. Tear chicken into thin strips.
Lay tortillas on a clean surface. Beginning about a quarter of the way up the middle of the tortilla, layer equal amounts of each ingredient, ending with a drizzle of the remaining lime juice. Fold up the bottom quarter of each tortilla and roll away from you, tucking in the sides as you go. Serve seam side down.