  We present photometric observations of an apparent Type Ia supernova (SN Ia)
at a redshift of ~1.7, the farthest SN observed to date. SN 1997ff, was
discovered in a repeat observation by the HST of the HDF-), and serendipitously
monitored with NICMOS on HST throughout the GTO campaign. The SN type can be
determined from the host galaxy type:an evolved, red elliptical lacking enough
recent star formation to provide a significant population of core-collapse SNe.
The class- ification is further supported by diagnostics available from the
observed colors and temporal behavior of the SN, both of which match a typical
SN Ia. The photo- metric record of the SN includes a dozen flux measurements in
the I, J, and H bands spanning 35 days in the observed frame. The redshift
derived from the SN photometry, z=1.7+/-0.1, is in excellent agreement with the
redshift estimate of z=1.65+/-0.15 derived from the
U_300,B_450,V_606,I_814,J_110,J_125,H_160, H_165,K_s photometry of the galaxy.
Optical and near-infrared spectra of the host provide a very tentative
spectroscopic redshift of 1.755. Fits to observations of the SN provide
constraints for the redshift-distance relation of SNe~Ia and a powerful test of
the current accelerating Universe hypothesis. The apparent SN brightness is
consistent with that expected in the decelerating phase of the preferred
cosmological model, Omega_M~1/3, Omega_Lambda~2/3. It is inconsistent with grey
dust or simple luminosity evolution, candidate astro- physical effects which
could mimic past evidence for an accelerating Universe from SNe Ia at z~0.5.We
consider several sources of possible systematic error including lensing, SN
misclassification, selection bias, and calibration errors. Currently, none of
these effects appears likely to challenge our conclusions.
