Blend 1 cup lime juice, garlic, achiote paste, oregano, and cumin in processor until smooth. Season marinade to taste with salt and pepper. Place marinade in medium bowl. Add chicken; stir to coat. Cover and refrigerate chicken overnight.

Preheat oven to 400 degrees. Place chilies on small baking sheet. Roast until soft, about 20 minutes. Stem and seed chilies. Transfer chilies to processor. Add pureed guava, reserved guava syrup, cilantro, and remaining 1/2 cup lime juice. Process until smooth. Season sauce to taste with salt and pepper. Transfer to medium bowl. (Sauce can be made 1 day ahead. Cover and refrigerate. Bring to room temperature before using.)

Prepare barbecue (medium-high heat). Remove chicken from marinade. Divide chicken among 8 eight-inch metal skewers. Grill until chicken is cooked, turning once, about 7 minutes. Serve, passing guava sauce separately.

This recipe yields 4 servings.