We report the discovery of the first short period binary in which a hot subdwarf star (sdOB) fills its Roche lobe and started mass transfer to its companion. The object was discovered as part of a dedicated high-cadence survey of the Galactic Plane named the Zwicky Transient Facility and exhibits a period of $P_{rm orb}=39.3401(1)$ min, making it the most compact hot subdwarf binary currently known. Spectroscopic observations are consistent with an intermediate He-sdOB star with an effective temperature of $T_{rm eff}=42,400pm300$ K and a surface gravity of $log(g)=5.77pm0.05$. A high-signal-to noise GTC+HiPERCAM light curve is dominated by the ellipsoidal deformation of the sdOB star and an eclipse of the sdOB by an accretion disk. We infer a low-mass hot subdwarf donor with a mass $M_{rm sdOB}=0.337pm0.015$ M$_odot$ and a white dwarf accretor with a mass $M_{rm WD}=0.545pm0.020$ M$_odot$. Theoretical binary modeling indicates the hot subdwarf formed during a common envelope phase when a $2.5-2.8$ M$_odot$ star lost its envelope when crossing the Hertzsprung Gap. To match its current $P_{rm orb}$, $T_{rm eff}$, $log(g)$, and masses, we estimate a post-common envelope period of $P_{rm orb}approx150$ min, and find the sdOB star is currently undergoing hydrogen shell burning. We estimate that the hot subdwarf will become a white dwarf with a thick helium layer of $approx0.1$ M$_odot$ and will merge with its carbon/oxygen white dwarf companion after $approx17$ Myr and presumably explode as a thermonuclear supernova or form an R CrB star.
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