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 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 \sim 10 ^ { 7 } K thermal plasma . Comparisons with the 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 \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } } 1 kpc from the Sun .