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Preheat grill.
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Place chicken breasts into a ziploc bag and pound to 1/2 inch thick.
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Remove chicken from bag and liberally season each side with chicken rub.
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In a small bowl mix together broccoli and all four cheeses until well combined.
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Place a 1/4 of the mixture on one end of chicken breast and roll up, securing with toothpicks.
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Repeat with remaining chicken breasts.
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Cook on grill for 5-7 minutes. Then flip.
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Cook other side for an additional 5-7 minutes or until chicken has reached an internal temperature of 165° F.
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Remove from grill and serve.