In a medium bowl, combine the chicken pieces with soy sauce, calamansi juice, minced garlic, grated ginger, and black pepper. Marinate for at least 30 minutes, or up to 2 hours in the refrigerator.
Heat the cooking oil in a large skillet or wok over medium-high heat. Add the marinated chicken and cook until browned on all sides and cooked through, about 5-7 minutes.
Add the sliced onions to the skillet with the chicken. Sauté until the onions are softened and slightly caramelized, about 3-4 minutes.
Serve the chicken and onion mixture immediately over warm jasmine rice.
Garnish with fresh cilantro and fried garlic bits, if desired.