We examine the host morphologies of heavily obscured active galactic nuclei (AGN) at $zsim1$ to test whether obscured supermassive black hole growth at this epoch is preferentially linked to galaxy mergers. Our sample consists of 154 obscured AGN with $N_{rm H}>10^{23.5}$ cm$^{-2}$ and $z<1.5$. Using visual classifications, we compare the morphologies of these AGN to control samples of moderately obscured ($10^{22}$ cm$^{-2}$ $<N_{rm H}< 10^{23.5}$ cm$^{-2}$) and unobscured ($N_{rm H}<10^{22}$ cm$^{-2}$) AGN. These control AGN are matched in redshift and intrinsic X-ray luminosity to our heavily obscured AGN. We find that heavily obscured AGN at z~1 are twice as likely to be hosted by late-type galaxies relative to unobscured AGN ($65.3^{+4.1}_{-4.6}%$ vs $34.5^{+2.9}_{-2.7}%$) and three times as likely to exhibit merger or interaction signatures ($21.5^{+4.2}_{-3.3}%$ vs $7.8^{+1.9}_{-1.3}%$). The increased merger fraction is significant at the 3.8$sigma$ level. We also find that the incidence of point-like morphologies is inversely proportional to obscuration. If we exclude all point sources and consider only extended hosts, we find the correlation between merger fraction and obscuration is still evident, however at a reduced statistical significance ($2.5sigma$). The fact that we observe a different disk/spheroid fraction versus obscuration indicates that viewing angle cannot be the only thing differentiating our three AGN samples, as a simple unification model would suggest. The increased fraction of disturbed morphologies with obscuration supports an evolutionary scenario, in which Compton-thick AGN are a distinct phase of obscured SMBH growth following a merger/interaction event. Our findings also suggest that some of the merger-triggered SMBH growth predicted by recent AGN fueling models may be hidden among the heavily obscured, Compton-thick population.
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