We report the discovery of a Type Ia supernova (SNIa) at redshift z=1.55 with the infrared detector of the Wide Field Camera 3 (WFC3-IR) on the Hubble Space Telescope (HST). This object was discovered in CANDELS imaging data of the Hubble Ultra Deep Field, and followed as part of the CANDELS+CLASH Supernova project, comprising the SN search components from those two HST multi-cycle treasury programs. This is the highest redshift SNIa with direct spectroscopic evidence for classification. It is also the first SN Ia at z>1 found and followed in the infrared, providing a full light curve in rest-frame optical bands. The classification and redshift are securely defined from a combination of multi-band and multi-epoch photometry of the SN, ground-based spectroscopy of the host galaxy, and WFC3-IR grism spectroscopy of both the SN and host. This object is the first of a projected sample at z>1.5 that will be discovered by the CANDELS and CLASH programs. The full CANDELS+CLASH SN Ia sample will enable unique tests for evolutionary effects that could arise due to differences in SN Ia progenitor systems as a function of redshift. This high-z sample will also allow measurement of the SN Ia rate out to z~2, providing a complementary constraint on SN Ia progenitor models.