Preheat a covered indoor grill. Meanwhile, split each roll in half horizontally. To assemble sandwiches, spread cut sides of roll halves with mayonnaise. Layer chicken, Canadian-style bacon, cheese, and spinach on bottom halves of rolls. Spread 1 to 2 tablespoons chutney on cut side of each roll top. Replace top halves of rolls.
Place sandwiches (half at a time if necessary) in grill, cover, and cook about 6 minutes or until cheese melts and rolls are crisp.