Preheat the oven to 425 degrees F.
For the sauce: In a medium bowl, combine the sour cream, mayonnaise, horseradish, mustard, salt, pepper and chives. Mix well. Let sit in refrigerator for at least 20 minutes before serving. (Can be made a day ahead.)
For the tenderloin: Place the parsley, rosemary, thyme, garlic and salt in a food processor. Pulse until finely chopped. Add 1/4 cup olive oil and pulse a few times to make a thick paste.
Heat a large skillet over high heat. Lightly brush the tenderloin with olive oil and sprinkle with black pepper. Sear on all sides, about 2 minutes per side. Rub the tenderloin with the herb mixture.
Place the pan into the oven; roast until the tenderloin reaches an internal temperature of 135 degrees F for medium, 35 to 40 minutes.
Remove from the oven, cover with foil and let rest for 10 minutes. Remove the string, slice, and serve with horseradish cream sauce.