On 23 October 2015 at ~1732 UTC, the Airborne Detector for Energetic Lightning Emissions (ADELE) flew through the eyewall of Hurricane Patricia aboard National Oceanic and Atmospheric Administration’s Hurricane Hunter WP‐3D Orion, observing the first terrestrial gamma‐ray flash (TGF) ever seen in that context, and the first ever viewed from behind the forward direction of the main TGF gamma‐ray burst. ADELE measured 184 counts of ionizing radiation within 150 μs, coincident with the detection of a nearby lightning flash. Lightning characteristics inferred from the associated radio signal and comparison of the gamma‐ray energy spectrum to simulations suggests that this is the first observation of a reverse beam of positrons predicted by the leading TGF production model, relativistic runaway electron avalanches. This paper presents the first experimental evidence of a previously predicted second component of gamma‐ray emission from TGFs. The brightest emission, commonly observed from orbit, is from the relativistic runaway electron avalanche bremsstrahlung; the second, fainter component reported here is from the bremsstrahlung of positrons propagating in the reverse direction. This reverse gamma‐ray beam penetrates to low enough altitudes to allow ground‐based detection of typical upward TGFs from mountain observatories.