To make the horseradish cream sauce, combine sour cream, mayonnaise, prepared horseradish and chives; season with salt and pepper, to taste. Set aside in the refrigerator until ready to serve.
Preheat oven to 275 degrees F. Line a baking sheet with foil and coat with nonstick spray.
In a small bowl, combine garlic, rosemary, thyme, 1 tablespoon salt and 1 tablespoon pepper.
Using paper towels, pat tenderloin dry. Drizzle with olive oil; season with garlic mixture, gently pressing to adhere.
Place tenderloin onto the prepared baking sheet. Place into oven and bake until it reaches an internal temperature of 130-135 degrees F for medium-rare, about 50 minutes to 1 hour and 15 minutes, or until desired doneness. Let rest 10 minutes before slicing.