Rinse rice under cold water. Place rice in slow cooker bowl and add the broth, chicken, shallot, carrot and celery. Cover and cook on LOW for about 5 hours or until rice kernels are open but not mushy.
Remove cover and stir in snap peas, vinegar, walnuts, parsley, salt and pepper.
Remove 12 small bowl-shaped leaves from head of lettuce; rinse and pat dry. Spoon about 1/2 cup rice mixture into each lettuce cup and serve.