  We present new far-ultraviolet spectra from the Cosmic Origins Spectrograph
(HST/COS) of the BL Lac object 1ES1553+113 covering the wavelength range
1135-1795 A. The data show a smooth continuum with a wealth of narrow
absorption features arising in the ISM and IGM. These features include 41 Lya
absorbers at 0<z<0.43, fourteen of which are detected in multiple Lyman lines
and six in one or more metal lines. We analyze a metal-rich triplet of Lya
absorbers at z=0.188 in which OVI, NV, and CIII absorption is detected. Silicon
ions (SiIII/IV) are not detected to fairly strong upper limits, and we use the
measured SiIII/CIII upper limit to derive an abundance limit [C/Si]>0.6 for the
strongest component of the absorber complex. Galaxy redshift surveys show a
number of massive galaxies at approximately the same redshift as this
absorption complex, suggesting that it arises in a large-scale galaxy filament.
As one of the brightest extragalactic X-ray and gamma-ray sources, 1ES1553+113
is of great interest to the high-energy astrophysics community. With no
intrinsic emission or absorption features, 1ES1553+113 has no direct redshift
determination. We use intervening Lya absorbers to place a direct limit on the
redshift: z_em>0.395 based on a confirmed Lya+OVI absorber and z_em>0.433 based
on a single-line detection of Lya. COS/FUV data are only sensitive to Lya
absorbers at z<0.47, but we present statistical arguments that z_em<0.58 based
on the non-detection of any Lyb absorbers at z>0.4.
