Heat oil in a large skillet over medium-high heat. Add garlic and cook 1 minute. Season chicken on both sides with salt and pepper and add to skillet. Cook until browned on all sides, stirring frequently, about 4 minutes.
Add 1 cup of broth, soy sauce, celery, bamboo shoots and water chestnuts to chicken and bring to a simmer. Reduce heat to low, cover and simmer until chicken is cooked through, about 5 minutes.
Dissolve cornstarch in remaining 1/2 cup of broth. Add cornstarch mixture to skillet and simmer until sauce thickens, stirring constantly, about 1 minute.
To serve, divide rice among 4 shallow dishes. Spoon chicken mixture onto rice and sprinkle with cashews. Yields about 1 cup of chicken, 1/2 cup of rice and 1 1/2 tablespoons of cashews per serving.
For a flavor boost, add 2 cups of chopped fresh baby bok choy in place of the bamboo shoots and water chestnuts. The tender greens will cook with the chicken in 5 minutes.