Mix together softened cream cheese, chopped green onions and shredded pepperjack cheese. Put 1/4 of this mixture into the middle of each piece of chicken.
Starting at the long side, roll chicken breast up, keeping the cheese mixture to the middle.
Wrap 1 to 2 slices of bacon around the chicken breast, secure with toothpick, if needed.
One piece of bacon wrapped around each breast is enough. But 2 pieces of bacon for each breast fully wraps the chicken and is outstanding.
Place on baking sheet and back for 30 minutes at 375 degrees F.
Broil topside for about 5 minutes to fully brown and crisp bacon. Turn each breast over and broil for another 3 minutes or so to crisp up the bottom side.