During hard X-ray observations of the Norma spiral arm region by the Nuclear Spectroscopic Telescope Array (NuSTAR) in 2013 February, a new transient source, NuSTAR J163433-4738.7, was detected at a significance level of 8-sigma in the 3-10 keV bandpass. The source is consistent with having a constant NuSTAR count rate over a period of 40 ks and is also detected simultaneously by Swift at lower significance. The source is not significantly detected by NuSTAR, Swift, or Chandra in the days before or weeks after the discovery of the transient, indicating that the strong X-ray activity lasted for between ~0.5 and 1.5 days. Near-IR imaging observations were carried out before and after the X-ray activity, but we are not able to identify the counterpart. The combined NuSTAR and Swift energy spectrum is consistent with a power-law with a photon index of Gamma = 4.1(+1.5)(-1.0) (90% confidence errors), a blackbody with kT = 1.2+/-0.3 keV, or a bremsstrahlung model with kT = 3.0(+2.1)(-1.2) keV. The reduced-chi2 values for the three models are not significantly different, ranging from 1.23 to 1.44 for 8 degrees of freedom. The spectrum is strongly absorbed with NH = 2.8(+2.3)(-1.4)e23 cm-2, 9(+15)(-7)e22 cm-2, and 1.7(+1.7)(-0.9)e23 cm-2, for the power-law, blackbody, and bremsstrahlung models, respectively. Although the high column density could be due to material local to the source, it is consistent with absorption from interstellar material along the line of sight at a distance of 11 kpc, which would indicate an X-ray luminosity >1e34 erg/s. Although we do not reach a definitive determination of the nature of NuSTAR J163433-4738.7, we suggest that it may be an unusually bright active binary or a magnetar. ; Comment: 6 pages, 4 figures, published as ApJ, 785, 4. The name of the source has been revised to NuSTAR J163433-4738.7 in order to comply with the IAU format for NuSTAR sources