Heat grill to medium-high heat. Using paper towels, pat chicken dry. In large bowl, mix together chicken and olive oil, tossing to coat completely. Sprinkle chicken all over with adobo.
Place chicken on grill skin-side down. Cook until skin turns dark golden brown, about 10 minutes, checking after 5 min. Flip chicken; cook until chicken is cooked through (internal temperature will register 165°F on instant-read thermometer), about 10 minutes more.
To ensure your grill’s surface is hot enough to leave marks, try this temperature test. Hold the palm of your hand 4-5 inches over the grate. If it takes your hand 8-10 seconds to pull away from the heat, the temp is low, about 250°F. If your hand pulls away after 5-7 seconds, the heat is medium, about 350°F; 2-4 seconds and the grill is hot, about 450°F – the perfect searing temperature.