Heat 2 Tablespoons vegetable oil in 12 inch skillet until hot. Cook and stir chayote over medium heat until crisp-tender, about 5 minutes; remove from heat.
Cook and stir onion and garlic in 1 tablespoon oil until onion is tender, about 5 minutes. Stir in rice, cook and stir until hot, about 8 minutes. Stir in chayote, tomato, salt and pepper. Cook and stir until tomato is hot, 3 to 5 minutes. Sprinkle with chives.