  Filaments of the cosmic web have long been associated with the threadlike
structures seen in galaxy redshift surveys. However, despite their baryon
content being dominated by hot gas, these filaments have been an elusive target
for X-ray observations. Recently, detections of filaments in very deep (2.4
Msec) observations with Chandra were reported around Abell 133 (z=0.0559). To
verify these claims, we conducted a multi-object spectrographic campaign on the
Baade 6.5m telescope around Abell 133; this resulted in a catalog of
${\sim}3000$ new redshift measurements, of which 254 are of galaxies near the
cluster. We investigate the kinematic state of Abell 133 and identify the
physical locations of filamentary structure in the galaxy distribution.
Contrary to previous studies, we see no evidence that Abell 133 is dynamically
disturbed; we reject the hypothesis that there is a kinematically distinct
subgroup (p=0.28) and find no velocity offset between the central galaxy and
the cluster ($\textrm{Z}_\textrm{score}=0.041^{+0.111}_{-0.106}$). The spatial
distribution of galaxies traces the X-ray filaments, as confirmed by angular
cross correlation with a significance of ${\sim}5\sigma$. A similar agreement
is found in the angular density distribution, where two X-ray structures have
corresponding galaxy enhancements. We also identify filaments in the
large-scale structure of galaxies; these filaments approach the cluster from
the direction the X-ray structures are seen. While more members between
$\textrm{R}_{200}$ and $2\times\textrm{R}_{200}$ are required to clarify which
large scale filaments connect to the X-ray gas, we argue that this is
compelling evidence that the X-ray emission is indeed associated with cosmic
filaments.
