Heat the oil in a large skillet over medium heat. Add the onion and garlic; cook and stir until the onion has softened and turned translucent, about 5 minutes. Add the gingerroot and bell peppers; cook and stir for 2 minutes.
Season the chicken cubes with salt and pepper; add to the skillet. Cook and stir until lightly browned on all sides.
Stir in the peanut butter until smooth. Pour in the soy sauce; mix well. Reduce heat to low, cover skillet, and simmer for 10 minutes.