To prepare peanut sauce: In small bowl, whisk soy sauce, lime juice, rice vinegar and honey. Add peanut butter and sesame oil. Whisk vigorously until sauce is completely smooth and creamy. Set aside.
To prepare bowls: In nonstick 12-inch skillet over medium-high heat, heat olive oil until simmering. Add shredded chicken and about 3 tablespoons peanut sauce. Stir constantly to coat chicken and heat through, about 3 minutes. Remove from heat and set aside.
To assemble rice bowls: In deep serving bowls, add cooked rice. Top with warm chicken covered in peanut sauce. Arrange celery, carrot and cucumber around chicken. Top with peanuts.
Drizzle remaining peanut sauce over bowls. Serve with lime wedges to squeeze over bowls.