We report the identification of an extreme protocluster of galaxies in the early universe whose core (nicknamed Distant Red Core, DRC, because of its very red color in Herschel SPIRE bands) is formed by at least 10 dusty star-forming galaxies (DSFGs), spectroscopically confirmed to lie at {z}spec}=4.002 via detection of [C I](1–0), 12CO(6–5), 12CO(4–3), 12CO(2–1), and {{{H}}}2{{O}}({2}11{--}{2}02) emission lines with ALMA and ATCA. These DSFGs are distributed over a 260 {kpc}× 310 {kpc} region and have a collective obscured star formation rate (SFR) of ∼ 6500 {M}ȯ {yr}}-1, considerably higher than those seen before in any protocluster at z≳ 4. Most of the star formation is taking place in luminous DSFGs since no Lyα emitters are detected in the protocluster core, apart from a Lyα blob located next to one of the DRC components, extending over 60 {kpc}. The total obscured SFR of the protocluster could rise to {SFR}∼ {{14,400}} {M}ȯ {yr}}-1 if all the members of an overdensity of bright DSFGs discovered around DRC in a wide-field Large APEX BOlometer CAmera 870 μm image are part of the same structure. [C I](1–0) emission reveals that DRC has a total molecular gas mass of at least {M}{{{H}}2}∼ 6.6× {10}11 {M}ȯ , and its total halo mass could be as high as ∼ 4.4× {10}13 {M}ȯ , indicating that it is the likely progenitor of a cluster at least as massive as Coma at z = 0.