Whisk together lime juice, olive oil, onions, peppers, garlic, cilantro, and oregano.
Submerge the chicken breasts in the liquid and cover. Place in refrigerator and let stand for 2 to 3 hours or up to two days.
When ready to cook, take chicken out of liquid using tongs. Arrange the chicken on a baking sheet and place under preheated broiler or lay chicken on a heated grill. Cook the chicken 7 to 8 minutes on each side, make sure chicken is cooked through.
Scatter lime wedges around chicken before serving.