Context. Very low-mass stars are known to have jets and outflows, which is indicative of a scaled-down version of low-mass star formation. However, only very few outflows in very low-mass sources are well characterized. Aims. We characterize the bipolar molecular outflow of the very low-mass star Par-Lup3-4, a 0.12 M⊙ object known to power an optical jet. Methods. We observed Par-Lup3-4 with ALMA in Bands 6 and 7, detecting both the continuum and CO molecular gas. In particular, we studied three main emission lines: CO(2–1), CO(3–2), and 13CO(3–2). Results. Our observations reveal for the first time the base of a bipolar molecular outflow in a very low-mass star, as well as a stream of material moving perpendicular to the primary outflow of this source. The primary outflow morphology is consistent with the previously determined jet orientation and disk inclination. The outflow mass is 9.5 × 10−7 M⊙, with an outflow rate of 4.3 × 10−9 M⊙ yr−1. A new fitting to the spectral energy distribution suggests that Par-Lup3-4 may be a binary system. Conclusions. We have characterized Par-Lup3-4 in detail, and its properties are consistent with those reported in other very low-mass sources. This source provides further evidence that very low-mass sources form as a scaled-down version of low-mass stars.