Heat the olive oil in a small saucepan over medium-high heat until very hot. While the oil heats, mash the cumin, salt, oregano, and garlic together into a paste in a heat-proof bowl; whisk the hot oil into the paste. Allow the mixture to cool slightly. Add the lime juice and orange juice; stir. Place the chicken in a large sealable bag; pour the marinade over the chicken and shake to assure an even coating. Refrigerate at least 4 hours, up to overnight.
Preheat an oven to 375 degrees F (190 degrees C). Arrange the marinated chicken in a roasting pan.
Bake the chicken in the preheated oven until no longer pink at the bone and the juices run clear, about 1 hour. An instant-read thermometer inserted into the thickest part of the thigh, near the bone should read 180 degrees F (82 degrees C).