We report the discovery of a new Herbig–Haro jet, HH 1165, in SOAR narrow-band imaging of the vicinity of the σ Orionis cluster. HH 1165 shows a spectacular extended and collimated spatial structure, with a projected length of 0.26 pc, a bent C-shaped morphology, multiple knots, and fragmented bow shocks at the apparent ends of the flow. The Hα image shows a bright halo with a clumpy distribution of material seen around the driving source, and curved reflection nebulosity tracing the outflow cavities. The driving source of HH 1165 is a Class I proto-brown dwarf, Mayrit 1701117 (M1701117), with a total (dust+gas) mass of ~36 M Jup and a bolometric luminosity of ~0.1 L ⊙. High-resolution VLT/UVES spectra of M1701117 show a wealth of emission lines indicative of strong outflow and accretion activity. SOAR/Goodman low-resolution spectra along the jet axis show an asymmetrical morphology for HH 1165. We find a puzzling picture wherein the northwest part exhibits a classical HH jet running into a pre-dominantly neutral medium, while the southern part resembles an externally irradiated jet. The C-shaped bending in HH 1165 may be produced by the combined effects from the massive stars in the ionization front to the east, the σ Orionis core to the west, and the close proximity to the B2-type star HR 1950. HH 1165 shows all of the signatures to be considered as a scaled-down version of parsec-length HH jets, and can be termed as the first sub-stellar analog of a protostellar HH jet system.