  Context: The Subaru Deep Field (SDF) Supernova Survey discovered 10 Type Ia
supernovae (SNe Ia) in the redshift range 1.5<z<2.0, as determined solely from
photometric redshifts of the host galaxies. However, photometric redshifts
might be biased, and the SN sample could be contaminated by active galactic
nuclei (AGNs).
  Aims: We aim to obtain the first robust redshift measurement and
classification of a z > 1.5 SDF SN Ia host galaxy candidate
  Methods: We use the X-shooter (U-to-K-band) spectrograph on the Very Large
Telescope to allow the detection of different emission lines in a wide spectral
range.
  Results: We measure a spectroscopic redshift of 1.54563 +/- 0.00027 of
hSDF0705.25, consistent with its photometric redshift of 1.552 +/- 0.018. From
the strong emission-line spectrum we rule out AGN activity, thereby confirming
the optical transient as a SN. The host galaxy follows the fundamental
metallicity relation defined in Mannucci et al. (2010, 2011) showing that the
properties of this high-redshift SN Ia host galaxy is similar to other field
galaxies.
  Conclusions: Spectroscopic confirmation of additional SDF SN hosts would be
required to confirm the cosmic SN rate evolution measured in the SDF.
