  We search for the lensing signal of massive filaments between 135,000 pairs
of Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey. We develop a
new estimator that cleanly removes the much larger shear signal of the
neighboring LRG halos, relying only on the assumption of spherical symmetry. We
consider two models: a thick filament model constructed from ray-tracing
simulations for $\Lambda$CDM model, and a thin filament model which models the
filament by a string of halos along the line connecting the two LRGs. We show
that the filament lensing signal is in nice agreement with the thick simulation
filament, while strongly disfavoring the thin model. The magnitude of the
lensing shear due to the filament is below $10^{-4}$. Employing the likelihood
ratio test, we find a 4.5$\sigma$ significance for the detection of the
filament lensing signal, corresponding to a null hypothesis fluctuation
probability of $3 \times 10^{-6}$. We also carried out several null tests to
verify that the residual shear signal from neighboring LRGs and other shear
systematics are minimized.
