Preheat oven to 375 degrees F (190 degrees C). Season pork with salt and pepper.
Heat oil in an ovenproof skillet over high heat. Cook pork until browned on one side, 3 to 4 minutes. Turn over pork and transfer the skillet to the preheated oven. Cook until pork is browned and still slightly pink in the center, 20 to 25 minutes. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C). Transfer pork to a plate.
Remove any excess oil from the skillet and place it over medium-high heat. Pour in chicken broth and bring to a boil, scraping any browned bits off of the bottom of the pan. Whisk in cream, horseradish, Dijon mustard, and cayenne pepper. Continue cooking until the mixture is reduced to a thick sauce, 3 to 4 minutes. Remove from heat and whisk in cold butter. Stir in chives.
Slice pork into 1/2-inch slices and serve topped with sauce.