Heat the oil in a large skillet over medium heat; cook and stir the onion and garlic in the olive oil until fragrant, about 5 minutes. Stir the oyster sauce into the mixture; season with salt and pepper. Add the chicken and mix; cover and cook for 10 minutes. Add the tomato, carrot, and celery; cover again and cook another 5 minutes. Cook the chicken pieces until no longer pink at the bone and the juices run clear, an instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C). Fold the snow peas into the mixture.

Whisk the cornstarch and water together in a small bowl until no lumps remain; stir into the liquid in the skillet. Allow the mixture to simmer until the sauce has thickened, about 5 minutes. Serve hot.