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.
Pounding chicken to ¼” thickness helps it cook quickly and evenly. But if the thought of struggling with the mallet makes you want to skip the recipe altogether, instead, use your tortilla press to do the hard work! Place the chicken breast in zip-top plastic bag (or between two pieces of plastic wrap). Then, place the breast in the middle of the tortilla press and apply even pressure to flatten the chicken in a snap.