In a 3-quart saucepan, melt butter. Add shallots, celery, and garlic. Cook over medium heat until tender.
Stir flour into vegetable mixture. Cook and stir over medium heat for 3 minutes. Remove saucepan from heat. Using a wire whisk, stir in chicken broth or clam juice until smooth.
Add artichoke hearts, parsley, bay leaves, thyme, ground red pepper, salt, and pepper. Bring to boiling; reduce heat to low. Cover and simmer for 30 minutes. Remove and discard bay leaves. Add oysters and simmer, uncovered for 1 to 4 minutes or until oysters begin to curl around the edges.
Serves 8-10 side dish servings.