We report the discovery of ATLAS J101342.5−451656.8 (hereafter ATLAS J1013−4516), an 8.56 minute orbital-period mass-transferring AM Canum Venaticorum (AM CVn) binary with a mean Gaia magnitude of G = 19.51, identified via periodic variability in light curves from the Asteroid Terrestrial-impact Last Alert System (ATLAS) of Gaia white dwarf candidates. Follow-up with the Large Lenslet Array Magellan Spectrograph shows a helium-dominated accretion disk, and high-speed ULTRACAM photometry reveals pronounced primary and secondary eclipses. We construct a decade-long timing baseline leveraging light curves from the ATLAS and Gaia surveys, as well as the high-speed imagers ULTRACAM on the New Energy Telescope and proto-Lightspeed on the Magellan Clay telescope. From this timing baseline, we measure an orbital period derivative of Ṗ=−1.60±0.07×10−12 s s−1. Interpreted in the context of stable mass transfer, the magnitude and sign of Ṗ indicate that the orbital evolution is governed by the interplay between gravitational-wave-driven angular-momentum losses and mass transfer, directly probing the donor's structural response to mass loss. We constrain the accretor and donor mass based on stable mass-transfer arguments assuming angular-momentum loss dominated by gravitational-wave emission, allowing us to infer the characteristic gravitational wave strain of the binary for future space-based GW observatories such as the Laser Interferometer Space Antenna (LISA). We predict a characteristic strain corresponding to a 4 yr LISA signal-to-noise ratio ≳10, establishing ATLAS J1013−4516 as a strong prospective LISA source that will probe long-term orbital evolution in the mass-transferring regime.