We search the Planck data for a thermal Sunyaev-Zel'dovich (tSZ) signal due
to gas filaments between pairs of Luminous Red Galaxies (LRG's) taken from the
Sloan Digital Sky Survey Data Release 12 (SDSS/DR12). We identify $\sim$260,000
LRG pairs in the DR12 catalog that lie within 6-10 $h^{-1} \mathrm{Mpc}$ of
each other in tangential direction and within 6 $h^{-1} \mathrm{Mpc}$ in radial
direction. We stack pairs by rotating and scaling the angular positions of each
LRG so they lie on a common reference frame, then we subtract a circularly
symmetric halo from each member of the pair to search for a residual signal
between the pair members. We find a statistically significant (5.3$\sigma$)
signal between LRG pairs in the stacked data with a magnitude $\Delta y = (1.31
\pm 0.25) \times 10^{-8}$. The uncertainty is estimated from two Monte Carlo
null tests which also establish the reliability of our analysis. Assuming a
simple, isothermal, cylindrical filament model of electron over-density with a
radial density profile proportional to $r_c/r$ (as determined from
simulations), where $r$ is the perpendicular distance from the cylinder axis
and $r_c$ is the core radius of the density profile, we constrain the product
of over-density and filament temperature to be $\delta_c \times (T_{\rm e}/10^7
\, {\rm K}) \times (r_c/0.5h^{-1} \, {\rm Mpc}) = 2.7 \pm 0.5$. To our
knowledge, this is the first detection of filamentary gas at over-densities
typical of cosmological large-scale structure. We compare our result to the
BAHAMAS suite of cosmological hydrodynamic simulations (McCarthy et al. 2017)
and find a slightly lower, but marginally consistent Comptonization excess,
$\Delta y = (0.84 \pm 0.24) \times 10^{-8}$.