Mix the cream cheese and all but a tablespoon of the chives together in a small bowl until well combined. Season with salt and pepper.
Lay a slice of the salmon on a clean work surface with the shorter end closest to you. Gently spread an eighth of the cream cheese mixture thinly along the salmon leaving about 1/8-inch edge all around. Roll the salmon up like a jellyroll and cut into equal pieces. Repeat this process with the remaining ingredients. Serve sprinkled with the reserved chives.