We present near-infrared spectroscopy of the z=3.2 quasar SDSS J1707+6443, obtained with MOIRCS on the Subaru Telescope. This quasar is classified as a nitrogen-loud quasar because of the fairly strong NIII] and NIV] semi-forbidden emission lines from the broad-line region (BLR) observed in its rest-frame UV spectrum. However, our rest-frame optical spectrum from MOIRCS shows strong [OIII] emission from the narrow-line region (NLR) suggesting that, at variance with the BLR, NLR gas is not metal-rich. In order to reconcile these contradictory results, there may be two alternative possibilities; (1) the strong nitrogen lines from the BLR are simply due to a very high relative abundance of nitrogen rather than to a very high BLR metallicity, or (2) the BLR metallicity is not representative of the metallicity of the host galaxy, better traced by the NLR. In either case, the strong broad nitrogen lines in the UV spectrum are not indication of a chemically enriched host galaxy. We estimated the black hole mass and Eddington ratio of this quasar from the velocity width of both CIV and H_beta, that results in log(M_BH/M_sun) = 9.50 and log(L_bol/L_Edd) = -0.34. The relatively high Eddington ratio is consistent with our earlier result that strong nitrogen emission from BLRs is associated with high Eddington ratios. Finally, we detected significant [NeIII] emission from the NLR, implying a quite high gas density of n~10^6 cm^-3 and suggesting a strong coupling between quasar activity and dense interstellar clouds in the host galaxy.