Wash and clean Chayote shoots, removing tendrils and hard stems. Break stems into two-inch pieces. In a large pot bring two quarts of water to a boil.
Blanch chayote shoots in boiling water for 1 minute. Drain and cool in ice water.
In a wok or large frying pan, heat oil and butter. Add garlic and lightly brown over medium heat, stirring constantly. Do not let butter smoke. Add drained shoots and stir fry about three to four minutes; add salt and pepper flakes to taste. Serve immediately.
Pepper flakes may be omitted for people who do not like spicy food.