Heat grill to medium (350° to 450°). In a medium bowl, coat chicken with oil, salt, and spices. Grill chicken, turning once, until no longer pink in center, about 6 minutes total. Grill roll halves just until toasted and grill marks appear, about 1 minute.
Mix mayonnaise and blue cheese and spread 1 heaping tbsp. on cut sides of each roll. Assemble sandwiches with chicken, lettuce, and tomato.