  We present the first measurement of pulse scattering close to the eclipse
region of PSR B1957+20, which is in a compact binary system with a low-mass
star. We measured pulse scattering time-scales up to 0.2 ms close to the
eclipse and showed that it scales with the dispersion measure (DM) excess
roughly as $\tau\propto\Delta{\rm DM}^{2}$. Our observations provide the first
evidence of strong scattering due to multi-path propagation effects in the
eclipsing material. We show that Kolmogorov turbulence in the eclipsing
material with an inner scale of $\sim100$ m and an outer scale of the size of
the eclipse region can naturally explain the observation. Our results show that
the eclipsing material in such systems can be highly turbulent and suggest that
scattering is one of the main eclipsing mechanisms at around 1.4 GHz.
