About 1½ hours before you plan to barbecue, toss the chicken with the oil in a small bowl. Sprinkle the dry rub over it and stir to coat. Refrigerate, covered, for 1 hour.
Prepare the smoker for barbecuing, bringing the temperature to 200°F to 220°F.
Split the jalapeños along one side and seed them. Stuff a section of chicken breast and a sliver or tw