The initial multiplicity of stellar systems is highly uncertain. A number of mechanisms have been proposed to explain the origin of binary and multiple star systems, including core fragmentation, disk fragmentation and stellar capture. Observations show that protostellar and pre-main-sequence multiplicity is higher than the multiplicity found in field stars, which suggests that dynamical interactions occur early, splitting up multiple systems and modifying the initial stellar separations. Without direct, high-resolution observations of forming systems, however, it is difficult to determine the true initial multiplicity and the dominant binary formation mechanism. Here we report observations of a wide-separation (greater than 1,000 astronomical units) quadruple system composed of a young protostar and three gravitationally bound dense gas condensations. These condensations are the result of fragmentation of dense gas filaments, and each condensation is expected to form a star on a timescale of 40,000 years. We determine that the closest pair will form a bound binary, while the quadruple stellar system itself is bound but unstable on timescales of 500,000 years (comparable to the lifetime of the embedded protostellar phase). These observations suggest that filament fragmentation on length scales of about 5,000 astronomical units offers a viable pathway to the formation of multiple systems.