  To fully understand cosmic black hole growth we need to constrain the
population of heavily obscured active galactic nuclei (AGN) at the peak of
cosmic black hole growth ($z\sim$1-3). Sources with obscuring column densities
higher than $\mathrm{10^{24}}$ atoms $\mathrm{cm^{-2}}$, called Compton-thick
(CT) AGN, can be identified by excess X-ray emission at $\sim$20-30 keV, called
the "Compton hump". We apply the recently developed Spectral Curvature (SC)
method to high-redshift AGN (2<z<5) detected with Chandra. This method
parametrizes the characteristic "Compton hump" feature cosmologically
redshifted into the X-ray band at observed energies <10 keV. We find good
agreement in CT AGN found using the SC method and bright sources fit using
their full spectrum with X-ray spectroscopy. In the Chandra deep field south,
we measure a CT fraction of $\mathrm{17^{+19}_{-11}\%}$ (3/17) for sources with
observed luminosity $\mathrm{>5\times 10^{43}}$ erg $\mathrm{s^{-1}}$. In the
Cosmological evolution survey (COSMOS), we find an observed CT fraction of
$\mathrm{15^{+4}_{-3}\%}$ (40/272) or $\mathrm{32\pm11 \%}$ when corrected for
the survey sensitivity. When comparing to low redshift AGN with similar X-ray
luminosities, our results imply the CT AGN fraction is consistent with having
no redshift evolution. Finally, we provide SC equations that can be used to
find high-redshift CT AGN (z>1) for current (XMM-Newton) and future (eROSITA
and ATHENA) X-ray missions.
