We identify sources with extremely hard X-ray spectra (i.e., with photon indices of Γ 0.6 ) in the 13 deg2 NuSTAR serendipitous survey, to search for the most highly obscured active galactic nuclei (AGNs) detected at > 10 keV . Eight extreme NuSTAR sources are identified, and we use the NuSTAR data in combination with lower-energy X-ray observations (from Chandra, Swift XRT, and XMM-Newton) to characterize the broadband (0.5-24 keV) X-ray spectra. We find that all of the extreme sources are highly obscured AGNs, including three robust Compton-thick (CT; N H > 1.5 × 10 24 cm−2) AGNs at low redshift ( z < 0.1 ) and a likely CT AGN at higher redshift (z = 0.16). Most of the extreme sources would not have been identified as highly obscured based on the low-energy ( < 10 keV) X-ray coverage alone. The multiwavelength properties (e.g., optical spectra and X-ray-mid-IR luminosity ratios) provide further support for the eight sources being significantly obscured. Correcting for absorption, the intrinsic rest-frame 10-40 keV luminosities of the extreme sources cover a broad range, from 5 × 10 42 to 1045 erg s−1. The estimated number counts of CT AGNs in the NuSTAR serendipitous survey are in broad agreement with model expectations based on previous X-ray surveys, except for the lowest redshifts ( z < 0.07 ), where we measure a high CT fraction of f CT obs = 30 − 12 + 16 % . For the small sample of CT AGNs, we find a high fraction of galaxy major mergers (50% 33%) compared to control samples of "normal" AGNs.