Mince garlic and zest 1 lime and place into a small bowl. Set aside. Juice the 3 limes and place into another bowl. Set aside.
Cut chicken into evenly sized chunks. Place large pan or braising dish on stove and set to medium high. Add olive oil to pan, just enough to coat the bottom of the pan. Let oil heat up.
Once oil is really hot, add chicken chunks and let it cook, undisturbed. When the chicken has browned nicely on the bottom and no longer sticks to the pan, sprinkle chicken evenly with cumin and cayenne pepper. Let chicken cook for 1-2 more minutes. Flip chicken so it can brown on the other side.
Once it's browned, reduce heat to medium low and sprinkle with minced garlic and lime zest. Stir together with chicken to brown the garlic a little but don't let it burn!
Once chicken is cooked through, add lime juice to pan to help release the browned bits from the bottom of the pan (this releases all that extra flavor!). Give the chicken and lime juice a good stir and then let it cook for another 2 minutes, until the juice has reduced slightly. Serve with your favorite rice and beans for a well-rounded, satisfying meal.