A vibration damper for a chassis of a vehicle including a damper tube which is filled at least partially with damping liquid and in which a piston rod can be moved to and fro. A working piston is movable with the piston rod, by way of which working piston the interior space of the damper tube is divided into a piston rod-side working space and a working space which is remote from the piston rod. At least one additional attachment unit is connected to the damper tube in a fluid-tight manner by way of a throughflow element. The throughflow element is arranged on the damper tube in a direction which differs from the radial direction of the damper tube.