Cut chicken into 1−inch pieces. Marinade chicken with oyster sauce in a bowl and let stand for 10 minutes.
Combine sauce ingredients in a bowl.
Place a wok over high heat until hot. Add 2 tablespoons oil, swirling to coat sides. Add chilies and cook, stirring, until fragrant, about 10 seconds.
Add chicken and stir fry for 2 minutes. Remove chicken and chilies from wok.
Add remaining 1/2 tablespoon oil to wok, swirling to coat sides. Add garlic and cook, stirring, until fragrant, about 10 seconds. Add celery, bell pepper, and bamboo shoots; stir fry for 1 1/2 minutes.
Return chicken and chilies to wok; stir fry for 1 minute. Add sauce and bring to a boil. Add cornstarch solution and cook, stirring, until sauce boils and thickens. Add peanuts and stir to coat.