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In a small bowl, combine apple butter, brown sugar, apple cider vinegar, molasses, garlic, and sriracha. Whisk gently with a fork. Set about 1/3 of the mixture aside.
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Heat grill on a medium setting. While grill is preheating, trim extra fat from pork tenderloin. Place in a large glass baking dish (i.e. a large rectangular Pyrex) and sprinkle with kosher salt and freshly ground pepper. Keeping 1/3 of the sauce on the side, brush pork tenderloin with some of the remaining.
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Place pork on hot grill. Grill for 10 minutes, apply more sauce and flip. Apply additional sauce as needed, cooking until the pork reaches 150F in the thickest part.
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Remove pork tenderloin from grill and transfer to a clean Pyrex or cutting board. Allow to rest for 5 minutes, covered with foil.
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With a clean brush, brush pork with remaining sauce. Sprinkle with chives. Slice and serve hot.