Melt butter with oil in a large Dutch oven over medium-high heat; stir in flour, and cook, stirring constantly, 5 minutes or until caramel colored. Add onion and next 6 ingredients; sauté 5 minutes or until vegetables are tender.
Add chicken broth, parsley, and chives; cook, stirring constantly, 5 minutes or until mixture is thick and bubbly.
Stir in crawfish; cook 5 minutes or until thoroughly heated. Serve with hot cooked rice.
*2 lb. frozen cooked crawfish tails, thawed and drained, may be substituted for fresh.
