We show, both classically and quantum mechanically, enantioselective orientation of gas phase chiral molecules excited by laser fields with twisted polarization. Counterintuitively, the induced orientation, whose direction is laser controllable, does not disappear after the excitation, but stays approximately constant long after the end of the laser pulses, behavior unique to chiral systems. We computationally demonstrate this long-lasting orientation using propylene oxide molecules (CH3CHCH2O, or PPO) as an example, and consider two kinds of fields with twisted polarization: a pair of delayed cross-polarized pulses, and an optical centrifuge. This novel chiral effect opens new avenues for detecting molecular chirality, measuring enantiomeric excess and separating enantiomers with the help of inhomogeneous external fields.