We report the discovery of a new Herbig-Haro jet, HH 1165, in SOAR narrow-band imaging of the vicinity of the sigma 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 H alpha 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 similar to 36M(Jup) and a bolometric luminosity of similar to 0.1 L circle dot. 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 sigma 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.