  The current noise in a classical one-dimensional charge density wave system
is studied in the weak pinning regime by solving the overdamped equation of
motion numerically. At low temperatures and just above the zero temperature
depinning threshold, the power spectrum of the current noise $S(f)$ was found
to scale with frequency $f$ as $S(f) \sim f^{-\gamma}$, where $\gamma \approx
1$, suggesting the existence of {\it flicker noise}. Our result is in agreement
with experimental findings for quasi-one-dimensional charge density wave
systems and provides the first evidence of $1/f$ behavior obtained from first
principles.
