We identify sources with extremely hard X-ray spectra ( i.e. , with photon indices of \Gamma \lesssim 0.6 ) in the 13 deg ^ { 2 } NuSTAR serendipitous survey , to search for the most highly obscured 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 broad-band ( 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 \times 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–MIR 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 \approx 5 \times 10 ^ { 42 } to 10 ^ { 45 } 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 ^ { +16 } _ { -12 } \% . For the small sample of CT AGNs , we find a high fraction of galaxy major mergers ( 50 \pm 33 \% ) compared to control samples of “ normal ” AGNs .