1. Place chicken in a resealable plastic bag or glass dish.Chipotle Marinade:
2. In a food processor, blend chili sauce, chipotle chiles plus adobo sauce and lime juice. Add to chicken; turn to coat. Refrigerate for 30 minutes or up to several hours.
3. Remove chicken to a plate; scrape off and reserve marinade. Sauce: Transfer marinade to saucepan. Add molasses, brown sugar and vinegar. Bring to a boil over medium-high heat; boil 4 minutes. Set aside until ready to use.Quesadillas:
4. Heat gas grill to medium-high heat, or prepare charcoal grill with medium-hot coals. Cut onion into 1/2-inch-thick slices. Slide a skewer through each slice sideways to keep rings together. Brush both sides of onion with 1 tablespoon of the oil. Grill about 8 minutes per side, until lightly charred and tender. Transfer to a bowl; remove skewers. Separate into rings; cover bowl with plastic wrap. Set aside.
5. Grill chicken 5 to 8 minutes per side, until instant-read thermometer inserted in the thickest part registers 180 degrees F. Remove to cutting board; thinly slice, and place in a bowl. Stir in 1/2 cup sauce.
6. Top one tortilla with 2 tablespoons cheese, a generous 1/4 cup chicken, a few pieces of onion, 2 tablespoons cheese and a second tortilla. Brush both sides lightly with remaining oil. Grill 1 minute per side.
7. Serve with sour cream and extra sauce on the side.