We present a novel implementation for extremely high-resolution spectroscopy using custom-designed Fabry--Perot Interferometer (FPI) arrays. For a given telescope aperture at the seeing-limited case, these arrays can achieve resolutions well in excess of R ~ 105 using optical elements that are orders of magnitude smaller in size than standard echelle spectrographs of similar resolution. We apply this method specifically to the search for O2 in exoplanetary atmospheres using the O2 A band at 0.76 mum and show how an FPI array composed of ~10 etalons with parameters optimized for this science case can record R = 3--5 × 105 spectra covering the full O2 A band. Using simulated observations of the atmosphere of a transiting nearby Earth-like planet, we show how observations with an FPI array coupled to a long-slit spectrograph can reduce the number of transit observations needed to produce a 3sigma detection of O2 by ~30% compared to observations with an R = 105 echelle spectrograph. This in turn leads to a decrease in an observing program duration of several years. The number of transits needed for a 3sigma detection can be further reduced by increasing the efficiency of FPI arrays using dualons (an etalon with a buried reflective layer) and by coupling the FPI array to a dedicated spectrograph optimized for the O2 A band.
