The extremely neutron-deficient isotope $^{178}\mathrm{Pb}$ has been produced. The GREAT spectrometer at the focal plane position of the gas-filled separator RITU was used to study the $\ensuremath{\alpha}$ decay of $^{178}\mathrm{Pb}$ and its $\ensuremath{\alpha}$-decay chain through $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}$ correlations. The $\ensuremath{\alpha}$ decay was measured to have an energy and half-life of ${E}_{\ensuremath{\alpha}}$= 7610(30) keV and ${t}_{1/2}=0.{21}_{\ensuremath{-}0.08}^{+0.21}$ ms, respectively. The half-life is consistent with recent theoretical calculations using the Coulomb and proximity potential model. The $\ensuremath{\alpha}$-decay reduced width and hindrance factor for $^{178}\mathrm{Pb}$ were deduced and correspond to an unhindered $\mathrm{\ensuremath{\Delta}}l$ = 0 transition. In addition, the mass excess of $^{178}\mathrm{Pb}$ and the $\ensuremath{\alpha}$-decay $Q$ value were calculated from the experimental results and compared to theoretical values.