We study the properties of a sample of 211 heavily-obscured Active Galactic Nucleus ( AGN ) candidates in the Extended Chandra Deep Field-South selecting objects with f _ { 24 \mu m } / f _ { R } > 1000 and R - K > 4.5 . Of these , 18 were detected in X-rays and found to be obscured AGN with neutral hydrogen column densities of \sim 10 ^ { 23 } cm ^ { -2 } . In the X-ray undetected sample , the following evidence suggests a large fraction of heavily-obscured ( Compton Thick ) AGN : ( i ) The stacked X-ray signal of the sample is strong , with an observed ratio of soft to hard X-ray counts consistent with a population of \sim 90 % heavily obscured AGN combined with 10 % star-forming galaxies . ( ii ) The X-ray to mid-IR ratios for these sources are significantly larger than that of star-forming galaxies and \sim 2 orders of magnitude smaller than for the general AGN population , suggesting column densities of N _ { H } \gtrsim 5 \times 10 ^ { 24 } cm ^ { -2 } . ( iii ) The Spitzer near- and mid-IR colors of these sources are consistent with those of the X-ray-detected sample if the effects of dust self-absorption are considered . Spectral fitting to the rest-frame UV/optical light ( dominated by the host galaxy ) returns stellar masses of \sim 10 ^ { 11 } M _ { \odot } and < E ( B-V ) > =0.5 , and reveals evidence for a significant young stellar population , indicating that these sources are experiencing considerable star-formation . This sample of heavily-obscured AGN candidates implies a space density at z \sim 2 of \sim 10 ^ { -5 } Mpc ^ { -3 } , finding a strong evolution in the number of L _ { X } > 10 ^ { 44 } erg/s sources from z =1.5 to 2.5 , possibly consistent with a short-lived heavily-obscured phase before an unobscured quasar is visible .