Polycyclic aromatic hydrocarbons and related species have been suggested to play a key role in the astrochemical evolution of the interstellar medium, but the formation mechanism of even their simplest building block--the aromatic benzene molecule--has remained elusive for decades. Here we demonstrate in crossed molecular beam experiments combined with electronic structure and statistical calculations that benzene (C(6)H(6)) can be synthesized via the barrierless, exoergic reaction of the ethynyl radical and 1,3-butadiene, C(2)H + H(2)CCHCHCH(2) → C(6)H(6) + H, under single collision conditions. This reaction portrays the simplest representative of a reaction class in which aromatic molecules with a benzene core can be formed from acyclic precursors via barrierless reactions of ethynyl radicals with substituted 1,3-butadiene molecules. Unique gas-grain astrochemical models imply that this low-temperature route controls the synthesis of the very first aromatic ring from acyclic precursors in cold molecular clouds, such as in the Taurus Molecular Cloud. Rapid, subsequent barrierless reactions of benzene with ethynyl radicals can lead to naphthalene-like structures thus effectively propagating the ethynyl-radical mediated formation of aromatic molecules in the interstellar medium.