Preheat the oven to 200°F. Sprinkle the filet with salt all over.
Place the filet on a baking sheet in the center of the oven, and slow cook until it measures 115°F in the center, which will yield a medium-rare result, about 90 minutes. (This is best done with an integrated oven temperature probe. You can also periodically remove the filet and use a digital thermometer, measuring the temperature in the center of the beef.)
While the filet is slow cooking, prepare the horseradish crème fraiche. Mix the crème fraiche with the extra-hot horseradish in a bowl and refrigerate until serving.
Heat a heavy skillet or grill to high heat. Sear the filet on all sides, giving it a nice golden-brown color.
Allow the filet to rest at least 10 minutes, then slice and serve it topped with the horseradish crème fraiche and chives.