Quirks are generic predictions of strongly-coupled dark sectors. For weak-scale masses and a broad range of confining scales in the dark sector, quirks can be discovered only at the energy frontier, but quirk-anti-quirk pairs are produced with unusual signatures at low pT, making them difficult to detect at the large LHC detectors. We determine the prospects for discovering quirks using timing information at FASER, FASER2, and an “ultimate detector” in the far-forward region at the LHC. NLO QCD corrections are incorporated in the simulation of quirk production, which can significantly increase the production rate. To accurately propagate quirk pairs from the ATLAS interaction point to the forward detectors, the ionization energy loss of charged quirks traveling through matter, the radiation of infracolor glueballs and QCD hadrons during quirk pair oscillations, and the annihilation of quirkonium are properly considered. The quirk signal is separated from the large muon background using timing information from scintillator detectors by requiring either two coincident delayed tracks, based on arrival times at the detector, or two coincident slow tracks, based on time differences between hits in the front and back scintillators. We find that simple cuts preserve much of the signal, but reduce the muon background to negligible levels. With the data already collected, FASER can discover quirks in currently unconstrained parameter space. FASER2, running at the Forward Physics Facility during the HL-LHC era, will greatly extend this reach, probing the TeV-scale quirk masses motivated by the gauge hierarchy problem for the broad range of dark-sector confining scales between 100 eV and 100 keV.