Stir together cumin, salt, and pepper in a small bowl.
Combine cumin mixture, olive oil, lime juice, and garlic in a shallow dish or large zip-top plastic freezer bag; reserve remaining cumin mixture. Add chicken to dish or bag; cover or seal, and chill 8 hours or up to 24 hours, turning occasionally.
Bring all ingredients to a boil in a small saucepan over medium-high heat. Reduce heat to medium-low; simmer 7 minutes or until glaze thickens and reduces slightly, stirring often. Remove from heat; cool.
Heat a grill pan. Remove chicken from marinade, discarding marinade. Pat dry with paper towels. Rub reserved cumin mixture over chicken. Cook first with skin side up, for 4 minutes, brush each side with guava glaze. Remove from the pan and let chicken rest before serving.
Brush chicken with Guava Glaze. Grill, covered with grill lid, 30 more minutes or until meat thermometer inserted into thickest portion of thigh registers 180° and thickest portion of breast registers 170°, brushing every 10 minutes with glaze. Cut chicken halves in half between breast and thigh to make 8 serving-size pieces.
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