We present photometric observations of an apparent Type Ia supernova (SN Ia) at a redshift of approximately 1.7, the farthest SN observed to date. The supernova, SN 1997, was discovered in a repeat observation by the Hubble Space Telescope (HST) of the Hubble Deep Field{North (HDF-N), and serendipitously monitored with NICMOS on HST throughout the Thompson et al. 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 supernovae. The classification 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 photometric 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 plus or minus 0:1, is in excellent agreement with the redshift estimate of z = 1:65 plus or minus 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 approximately equal to 1/3; Omega_Lambda approximately equal to 2/3. It is inconsistent with grey dust or simple luminosity evolution, candidate astrophysical effects which could mimic previous evidence for an accelerating Universe from SNe Ia at z approximately equal to 0:5. We consider several sources of potential systematic error including gravitational lensing, supernova misclassification, sample selection bias, and luminosity calibration errors. Currently, none of these effects alone appears likely to challenge our conclusions. Additional SNe Ia at z > 1 will be required to test more exotic alternatives to the accelerating Universe hypothesis and to probe the nature of dark energy.