  We have obtained follow-up observations of the quasar pair LBQS 0107-025A,B
and new observations of the nearby quasar LBQS 0107-0232 with the Hubble Space
Telescope Faint Object Spectrograph. Extended wavelength coverage of LBQS
0107-025A and B using the G270H grating was also obtained. This triple system
is unique in providing sensitivity to coherent Ly-alpha absorption on
transverse scales of approximately 1 Mpc at z < 1. Monte Carlo simulations were
used to establish the confidence level for matches between absorption features
in different lines of sight as a function of velocity separation. Pairwise,
there are 8, 9, and 12 lines that match between spectra. Three instances of
matches between all three lines of sight were found with velocity separations
of less than 550 kms^-1. Two of the pairings have coincident lines within
|Delta v| < 200 kms^-1 that would occur with less than 10% probability by
chance. Taking into account the equivalent widths of the lines, one of these
triple coincidences is significant at the 99.99% confidence level, based on
Monte Carlo simulations with random line placements. Matches with strong lines
preferentially have small velocity separations. These same simulations are used
to demonstrate that the distribution of matches for a population of absorbers
randomly distributed in velocity space is peaked toward |Delta v| = 0, which
has implications for the statistical significance of matches. One of the triple
coincidences appears to be a strong absorber with a sheet-like, but
inhomogeneous, geometry and a coherence length approaching or exceeding 1 Mpc.
