Turn on broiler. Line a baking sheet with aluminum foil and set aside.
In a small saucepan, over medium-low heat, combine guava jelly, juice from lime, rosemary sprigs, and crushed garlic. Heat through.
In large frying pan, over medium-high heat, heat oil. Season chicken breasts with salt and pepper. Dredge seasoned chicken in flour and place in hot pan. Cook chicken 3 to 4 minutes per side or until cooked through.
Transfer to baking sheet. Strain guava mixture into a small bowl. Generously brush guava mixture over chicken breasts. Place under broiler 4 to 6 inches from heat source for 1 minute. Turn chicken over and repeat 2 times. Remove from broiler, brush once more with guava mixture. Serve hot.
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