  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 ${\rm R\sim10^5}$ using optical elements orders
of magnitude smaller in size than standard echelle spectrographs of similar
resolution. We apply this method specifically to the search for molecular
oxygen in exoplanetary atmospheres using the ${\rm O_2}$ A-band at 0.76 ${\rm
\mu m}$, and show how a FPI array composed of $\sim10$ etalons with parameters
optimized for this science case can record ${\rm R=3-5\,\cdot10^5}$ spectra
covering the full ${\rm O_2}$ A-band. Using simulated observations of the
atmosphere of a transiting nearby Earth-like planet, we show how observations
with a FPI array coupled to a long-slit spectrograph can reduce the number of
transit observations needed to produce a ${\rm 3\sigma}$ detection of ${\rm
O_2}$ by $\sim30\%$ compared to observations with a ${\rm R=10^5}$ echelle
spectrograph. This, in turn, leads to a decrease in an observing program
duration of several years. The number of transits needed for a ${\rm 3\sigma}$
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 ${\rm O_2}$ A-band.
