In a small saucepan, combine the orange juice, lime juice and chili pepper and bring to a boil. Reduce the heat to medium and simmer, uncovered, until the chili is plump, about 5 minutes. Remove from the heat and let cool. Transfer the cooled citrus mixture to a blender and add the salsa, olive oil and salt. Puree until smooth.
Rinse the chicken breasts and pat dry. Place the chicken breasts in a shallow non-aluminum dish. Pour the puree evenly over the top, cover and let marinate in the refrigerator for 2-4 hours.
Prepare a fire in a charcoal grill or preheat a broiler (griller). When the fire is hot or the broiler is ready, remove the chicken breasts from the marinade. Place them skin side down on the grill rack about 5 inches (13 cm) from the coals, or arrange them skin side up on a broiler pan and place in the broiler about 4 inches (10 cm) from the heat source.
Grill or broil for 2-3 minutes. Turn and cook on the second side for 2-3 minutes. Continue to cook the chicken, turning every 2-3 minutes to avoid burning, until tender and opaque throughout. The total cooking Transfer the chicken to a warmed platter. Garnish with orange slices and cilantro sprigs, if desired, and serve immediately.