Mix soy sauce, ketchup, ginger, and garlic in a re-sealable heavy-duty plastic bag.
Add chicken; seal bag and turn to coat with marinade.
Let stand 15 minutes.
Heat 1 tablespoon of the oil in 10-inch skillet or wok over medium-high heat.
Add bitter melon, green onions, and bell peppers; stir-fry until crisp-tender.
Remove from skillet. Heat the remaining 1 tablespoon oil in a skillet.
Add chicken; stir-fry 4 to 5 minutes or until no longer pink in center.
Stir in bell pepper mixture.
Serve over rice.
Parboiling bitter melon: Bring a large pot of water to a boil. Cut the ends off the bitter melon and cut in half lengthwise (do not peel). Remove the seeds and white pith from the middle of the melon with a small spoon. Cut the melon diagonally into thin, 1/4-inch slices. Place the sliced bitter melon in the boiling water and parboil until it is just tender (2 - 3 minutes). Drain.