In a blender combine pineapple, onion, cilantro, lime juice, tamari or soy sauce, garlic, and salt. Blend until smooth.
Place steak in a zip-top bag and pour in marinade. Seal bag, making sure steak is evenly coated. Place bag in a bowl in the refrigerator and marinate 2-5 hours (no longer or pineapple will negatively affect texture of steak).
Just before grilling steak, prepare chimichurri. In a medium bowl stir to combine avocado, cilantro, oil, vinegar, onion, and garlic. Add salt to taste and set aside.
Prepare a hot grill fire, preheat a gas grill on high heat for 10 minutes, or preheat an indoor grill or a grill pan over medium-high heat until very hot.
Remove steak from marinade, allowing excess to drip off. Grill steak, turning once, until well browned on both sides and cooked to desired degree of doneness (130-135℉ for medium-rare, 140℉ for medium, or 145-155℉ for well done). Transfer to a cutting board to rest for 5 minutes, then thinly slice across the grain.
Serve steak with avocado chimichurri.