  The diffuse X-ray background (DXB) emission near the Galactic plane ($l,b
\sim 25.6^{\circ},0.78^{\circ}$) has been observed with $ASCA$. The observed
region is toward a Galactic molecular cloud which was recently reported to cast
a deep X-ray shadow in the 0.5 $-$ 2.0 keV band DXB. The selection of this
particular region is intended to provide a constraint on the spatial
distribution of the DXB emission along the line of sight: i.e., the molecular
cloud is optically thick at $<$2 keV and so the bulk of the observed soft
X-rays {\it must} originate in the foreground of the cloud, which is at $\sim$3
kpc from the Sun. In the 0.8 $-$ 9.0 keV band, the observed spectrum is
primarily from multiple components of thermal plasmas. We here report a
detection of soft X-ray (0.5 $-$ 2 keV) emission from an $\sim10^{7}$ K thermal
plasma. Comparisons with the {\it ROSAT} data suggest that this soft X-ray
emission is absorbed by $N_H$ = 1 $-$ 3 $\times$ 10$^{21}$ cm$^{-2}$, which
implies a path-length through the soft X-ray emitting regions of $\la$1 kpc
from the Sun.
