To prepare salsa, combine the first 7 ingredients in a medium bowl. Cover and chill 1 hour.
To prepare chicken, preheat grill.
Combine oregano and next 10 ingredients (through 1/4 teaspoon salt) in a large zip-top plastic bag. Add chicken to bag; seal. Marinate chicken in refrigerator 1 hour, turning occasionally.
Remove chicken from bag; discard marinade. Place chicken on grill rack coated with cooking spray; grill 6 minutes on each side or until chicken is done. Serve with salsa.