Place chicken breast between plastic wrap sheets; using mallet, pound chicken to ¼” thickness; repeat with remaining breasts. Season chicken with adobo. Heat 2 tbsp. oil in large skillet over medium-high heat. Add chicken; cook until light golden brown on both sides, flipping once, about 7 minutes; set aside.
Add onions; cook until soft and translucent, about 10 minutes. Add garlic and oregano to pan; cook until fragrant, about 30 seconds more. Add tomato sauce, 1 cup water, olives, capers, bay leaf and jalapeños to pan; bring tomato sauce mixture to boil.
Transfer chicken to pan; cook, flipping once, until coated in sauce and cooked through, about 15 minutes more. Remove chicken from pan; stir remaining oil into tomato sauce mixture.
To serve, divide chicken and sauce evenly among serving dishes; sprinkle with cilantro. Serve with rice and lime wedge.
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