Pound the chicken breasts as thinly and as evenly as possible.
Spread the chicken with softened cream cheese and season.
Top with 3 pepper strips and 1 cheese log.
Using a strip of bacon at one end, tuck in the sides of the chicken and roll up lengthwise as tightly as possible, using the bacon to keep the roll together. Use toothpicks if necessary. Add another 1/2 piece of bacon to finish the length of the roll if necessary.
Place chicken roll on a square of saran and roll it up in the saran as tightly as possible.
Refrigerate rolls at least 2 hours to help them maintain their shape when cooking.
Heat grill to medium, remove saran wrap and grill chicken rolls for about 30 minutes* basting with BBQ sauce during the last few minutes. Remove toothpicks before serving.