Electron-capture delayed fission ECDF was studied in the new isotope $^{238}\mathrm{Bk}$ produced via the $^{241}\mathrm{Am}$(75-MeV \ensuremath{\alpha}, 7n${)}^{238}$Bk reaction. The half-life of the fission activity was measured to be 144\ifmmode\pm\else\textpm\fi{}5 seconds. The mass-yield distribution is predominantly asymmetric and the most probable preneutron emission total kinetic energy of fission is 179\ifmmode\pm\else\textpm\fi{}7 MeV. The ECDF mode in $^{238}\mathrm{Bk}$ was verified by an x-ray-fission coincidence experiment which indicated that the $^{238}\mathrm{Cm}$ fission lifetime is between about ${10}^{\mathrm{\ensuremath{-}}15}$ and ${10}^{\mathrm{\ensuremath{-}}9}$ seconds. The isotope was assigned to $^{238}\mathrm{Bk}$ through chemical separation and observation of the known 2.4-h $^{238}\mathrm{Cm}$ daughter activity. No alpha branch was observed in the decay of $^{238}\mathrm{Bk}$. The production cross section for $^{238}\mathrm{Bk}$ is 150\ifmmode\pm\else\textpm\fi{}20 nb and the delayed fission probability is (4.8\ifmmode\pm\else\textpm\fi{}2)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$.