  We report the detection of two CH$_3$OH lines (J$_K$ = 2$_K$-1$_K$ and
3$_K$-2$_K$) between the progenitor's disks ("Overlap") of the mid-stage
merging galaxy VV 114 obtained using the Atacama Large Millimeter/submillimeter
Array (ALMA) Band 3 and Band 4. The detected CH$_3$OH emission show an extended
filamentary structure (~ 3 kpc) across the progenitor's disks with relatively
large velocity width (FWZI ~ 150 km/s). The emission is only significant in the
"overlap" and not detected in the two merging nuclei. Assuming optically-thin
emission and local thermodynamic equilibrium (LTE), we found the CH$_3$OH
column density relative to H$_2$ ($X_{\rm CH_3OH}$) peaks at the "Overlap" (~ 8
$\times$ 10$^{-9}$), which is almost an order of magnitude larger than that at
the eastern nucleus. We suggest that kpc-scale shocks driven by galaxy-galaxy
collision may play an important role to enhance the CH$_3$OH abundance at the
"Overlap". This scenario is consistent with that shock-induced large velocity
dispersion components of ionized gas have been detected in optical wavelength
at the same region. Conversely, low $X_{\rm CH_3OH}$ at the nuclear regions
might be attributed to the strong photodissociation by nuclear starbursts
and/or putative active galactic nucleus (AGN), or inefficient production of
CH$_3$OH on dust grains due to initial high temperature conditions (i.e.,
desorption of the precursor molecule, CO, into gas-phase before forming
CH$_3$OH on dust grains). These ALMA observations demonstrate that CH$_3$OH is
a unique tool to address kpc-scale shock-induced gas dynamics and star
formation in merging galaxies.
