Heat the olive oil in a large skillet over medium heat.
Season the chicken with salt and pepper, then cook for 5-6 minutes until browned and cooked through.
Add chopped bell peppers and onion. Sauté for 3-4 minutes until just tender.
Stir in the garlic and cook for another 30 seconds.
In a bowl, whisk together ketchup, rice vinegar, soy sauce, brown sugar, cornstarch, and water.
Pour the sauce into the skillet and stir to coat all ingredients evenly.
Bring to a boil, then reduce heat and simmer for 5-6 minutes until the sauce thickens.
Serve hot over white rice if desired.