“He that strikes the venison first shall be the lord o’ the feast.” — Shakespeare, King Lear
Season the meat with salt and pepper. In a small bowl, mix herbs with the olive oil, then spread all over the meat. Refrigerate for at least 2 hours.
Make a hot fire in a charcoal grill or set a gas grill on high. Grill the meat on one side, without moving it, 4 to 5 minutes, then rotate 90 degrees to make grill marks and char more surface area. Flip the loin and cook 4 to 5 minutes more. It should have a deep-brown char on the outside but still be rare on the inside. Transfer to a warm plate and allow to rest for 10 minutes.
Mix the crème fraîche, horseradish, chives, lemon juice, and zest in a small bowl and season with salt. Serve the loin, thinly sliced against the grain, with the sauce.