Motor vehicle vibration damper

A motor vehicle vibration damper, comprising:

• at least one damping cylinder that is at least partially filled with a liquid damping medium,
• a piston rod that is axially movable with respect to the longitudinal axis (L) of the motor vehicle vibration damper and protrudes sectionally into the damping cylinder,
• a piston rod guide that encloses the piston rod, in the circumferential direction and seals the damping cylinder to the outside,
• a gas-impermeable, shape-changing gas pressure container, wherein the gas pressure container is arranged in a compensation chamber within the damping cylinder,
• a filling channel that connects the gas pressure container interior to the outside environment,
• and a check valve which is at least indirectly connected to the gas pressure container and which opens or closes the filling channel depending on a gas pressure difference between the gas pressure within the gas pressure container interior and the gas pressure outside the gas pressure container interior, wherein the check valve is designed within a gas-impermeable check valve housing which is connected to the piston rod guide in a form-fitting and/or substance-bonded manner.