  We present the redshift lower limit of z>0.6035 for the very-high-energy
(VHE; E>100 GeV) emitting blazar PKS 1424+240 (PG 1424+240). This limit is
inferred from Lyman beta and gamma absorption observed in the far-ultraviolet
spectra from the Hubble Space Telescope/Cosmic Origins Spectrograph. No
VHE-detected blazar has shown solid spectroscopic evidence of being more
distant. At this distance, VHE observations by VERITAS are shown to sample
historically large gamma-ray opacity values at 500 GeV, extending beyond tau=4
for low-level models of the extragalactic background light (EBL) and beyond
tau=5 for high-levels. The majority of the z=0.6035 absorption-corrected VHE
spectrum appears to exhibit a lower flux than an extrapolation of the
contemporaneous LAT power-law fit beyond 100 GeV. However, the highest energy
VERITAS point is the only point showing agreement with this extrapolation,
possibly implying the overestimation of the gamma-ray opacity or the onset of
an unexpected VHE spectral feature. A curved log parabola is favored when
fitting the full range of gamma-ray data (0.5 to 500 GeV). While fitting the
absorption-corrected VHE data alone results in a harder differential power law
than that from the full range, the indices derived using three EBL models are
consistent with the physically motivated limit set by Fermi acceleration
processes.
