Based　on　time-dependent　variational-principle　algorithms,　we　investigate　the　dynamical　critical　behavior　of　quantum　three-state　Potts　chains　with　chiral　interactions.　Using　the　Loschmidt　echo,　dynamical　order　parameter,　and　entanglement　entropy　as　an　indicator,　we　show　that　as　the　chiral　interaction　θ　increases,　the　first　critical　time　t1∗　shifts　towards　lower　values,　indicating　a　chirality-related　dynamical　phase　transition.　Moreover,　we　perform　dynamical　scaling　for　the　Loschmidt　echo　and　obtain　the　critical　exponent　ν　at　the　nonconformal　critical　point.　The　results　show　that　as　the　chiral　interaction　θ　increases,　the　correlation-length　exponent　ν　decreases,　which　is　similar　to　the　long-range　interaction　case.　Finally,　we　give　a　simple　physical　argument　to　understand　the　above　numerical　results.　This　work　provides　a　useful　reference　for　further　research　on　many-body　physics　out　of　equilibrium　with　chiral　interaction.　　©　2023　American　Physical　Society.