Combine first 5 ingredients in a large zip-top plastic bag. Add chicken to bag; seal. Marinate in refrigerator 3 hours, turning occasionally.
Prepare grill to medium-high heat.
Combine mayonnaise, rosemary, and garlic; set aside.
Remove chicken from bag, discarding marinade. Sprinkle chicken with salt. Place chicken on grill rack coated with cooking spray; grill 5 minutes on each side or until done. Remove chicken from grill. Place bell pepper and onion on grill rack coated with cooking spray; grill 6 minutes on each side or until slightly charred. Cut chicken diagonally across grain into thin slices. Separate onion into rings; cut bell pepper into thin strips.
Spread mayonnaise mixture evenly over cut sides of bottom and top halves of bread. Arrange cheese evenly over bottom half of bread. Arrange onion, bell pepper, and hearts of palm evenly over cheese; top with chicken and arugula. Place top half of bread over arugula. Cut filled baguette in half. Wrap each half tightly in plastic wrap. Place filled baguette halves in refrigerator; top with a cast-iron skillet or other heavy object. Let chill at least 2 hours. Cut each filled baguette half into 3 equal portions.