ABSTRACT We introduce a new color selection technique to identify high-redshift, massive galaxies that are systematically missed by Lyman-break selection. The new selection is based on the H160 (H) and Infrared Array Camera (IRAC) 4.5 m bands, specifically mag. These galaxies, called "HIEROs," include two major populations that can be separated with an additional J − H color. The populations are massive and dusty star-forming galaxies at ( ) and extremely dusty galaxies at ( ). The 350 arcmin2 of the GOODS-North and GOODS-South fields with the deepest Hubble Space Telescope (HST)/Wide Field Camera 3 (WFC3) near-infrared and IRAC data contain as many as 285 HIEROs down to mag. Inclusion of the most extreme HIEROs, not even detected in the H band, makes this selection particularly complete for the identification of massive high-redshift galaxies. We focus here primarily on ( ) HIEROs, which have a median photometric redshift and stellar mass and are much fainter in the rest-frame UV than similarly massive Lyman-break galaxies (LBGs). Their star formation rates (SFRs), derived from their stacked infrared spectral energy distributions (SEDs), reach ∼240 yr−1, leading to a specific SFR, Gyr−1, suggesting that the sSFRs for massive galaxies continue to grow at but at a lower growth rate than from z = 0 to z = 2. With a median half-light radius of 2 kpc, including as compact as quiescent (QS) galaxies at similar redshifts, HIEROs represent perfect star-forming progenitors of the most massive ( ) compact QS galaxies at and have the right number density. HIEROs make up of all galaxies with identified at from their photometric redshifts. This is five times more than LBGs with nearly no overlap between the two populations. While HIEROs make up 15%-25% of the total SFR density at -5, they completely dominate the SFR density taking place in galaxies, and HIEROs are therefore crucial to understanding the very early phase of massive galaxy formation.