In food processor, combine spinach, tomatoes, lime juice, onion and jalapeno (if using). Pulse to combine. Add avocados and cilantro and blend until well combined (mixture will be slightly lumpy).
Arrange tortillas on a clean surface. Spread about 1/4 cup (50ml) of the avocado mixture over half of each tortilla. Top with chicken; sprinkle with cheese. Fold each tortilla in half to cover filling.
Heat large skillet over medium heat. Arrange 2 quesadillas in the skillet and brown on both sides, about 3 minutes per side. Repeat with remaining quesadillas. Serve warm with remaining guacamole.
Per serving: about 280 calories, 10 g protein, 15 g fat (3 g saturated fat), 28 g carbohydrate, 4 g fiber, 15 mg cholesterol, 270 mg sodium. %RDI: 2% calcium, 10% iron, 20% vitamin A, 35% vitamin C.