Saute coconut, onion and celery in butter in heavy saucepan over medium-high heat until lightly browned, about 4 minutes. Add rice; toss to coat. Add vegetable broth, salt and pepper; stir to separate grains of rice. Bring to a boil. Reduce heat to low; cover; simmer 40 minutes or until rice is tender and all liquid has been absorbed. Do not stir.
Pour sesame oil and water chestnuts over top. Remove from heat; cover with lid. Let stand for 5 minutes. Fluff with fork. Garnish with green onions.