We present the results and the source catalog of the NuSTAR survey in the UKIDSS Ultra Deep Survey (UDS) field, bridging the gap in depth and area between NuSTAR's ECDFS and COSMOS surveys. The survey covers a similar to 0.6 deg(2) area of the field for a total observing time of similar to 1.75 Ms, to a half-area depth of similar to 155 ks corrected for vignetting at 3-24 keV, and reaching sensitivity limits at half-area in the full (3-24 keV), soft (3-8 keV), and hard (8-24 keV) bands of 2.2 x 10(-14) erg cm(-2) s(-1), 1.0 x 10(-14) erg cm(-2) s(-1), and 2.7 x 10(-14) erg cm(-2) s(-1), respectively. A total of 67 sources are detected in at least one of the three bands, 56 of which have a robust optical redshift with a median of < z > similar to 1.1. Through a broadband (0.5-24 keV) spectral analysis of the whole sample combined with the NuSTAR hardness ratios, we compute the observed Compton-thick (CT; N-H > 10(24) cm(-2)) fraction. Taking into account the uncertainties on each N-H measurement, the final number of CT sources is 6.8 +/- 1.2. This corresponds to an observed CT fraction of 11.5% +/- 2.0%, providing a robust lower limit to the intrinsic fraction of CT active galactic nuclei and placing constraints on cosmic X-ray background synthesis models.