Our understanding of the redshift z > 3 galaxy population relies largely on samples selected using the popular “ dropout ” technique , typically consisting of UV-bright galaxies with blue colors and prominent Lyman breaks . As it is currently unknown if these galaxies are representative of the massive galaxy population , we here use the FourStar Galaxy Evolution ( ZFOURGE ) Survey to create a stellar mass-limited sample at z = 3 - 4 . Uniquely , ZFOURGE uses deep near-infrared medium-bandwidth filters to derive accurate photometric redshifts and stellar population properties . The mass-complete sample consists of 57 galaxies with log M > 10.6 , reaching below M ^ { \star } at z = 3 - 4 . On average , the massive z = 3 - 4 galaxies are extremely faint in the observed optical with median R _ { tot } ^ { AB } = 27.48 \pm 0.41 ( restframe M _ { 1700 } = -18.05 \pm 0.37 ) . They lie far below the UV luminosity-stellar mass relation for Lyman break galaxies and are about \sim 100 \times fainter at the same mass . The massive galaxies are red ( R - Ks _ { AB } = 3.9 \pm 0.2 ; restframe UV-slope \beta = -0.2 \pm 0.3 ) likely from dust or old stellar ages . We classify the galaxy SEDs by their restframe U - V and V - J colors and find a diverse population : 46 ^ { +6 + 10 } _ { -6 - 17 } % of the massive galaxies are quiescent , 40 ^ { +6 + 7 } _ { -6 - 5 } % are dusty star-forming galaxies , and only 14 ^ { +3 + 10 } _ { -3 - 4 } % resemble luminous blue star forming Lyman break galaxies . This study clearly demonstrates an inherent diversity among massive galaxies at higher redshift than previously known . Furthermore , we uncover a reservoir of dusty star-forming galaxies with 4 \times lower specific star-formation rates compared to submillimeter-selected starbursts at z > 3 . With 5 \times higher numbers , the dusty galaxies may represent a more typical mode of star formation compared to submillimeter-bright starbursts .