In a medium bowl, whisk together lime juice, orange juice, soy sauce, Worcestershire sauce, brown sugar, garlic, cumin, salt, and pepper.
Place chicken breasts in a large resealable plastic bag or shallow dish and pour the marinade over them. Seal or cover and refrigerate for at least 2 hours, preferably overnight.
Preheat your grill to medium-high heat.
Remove chicken from marinade and discard the excess liquid.
Grill chicken for about 5–7 minutes per side, or until fully cooked and the internal temperature reaches 165°F (75°C).
Let rest for a couple of minutes before serving. Optional: squeeze a bit of fresh lime juice over the top for a final zing.