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　0　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　nu　at　the　nonconformal　critical　point.　The　results　show　that　as　the　chiral　interaction　0　increases,　the　correlation-length　exponent　nu　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.