Useful insights into the complicated physics of gravitational waves can often be drawn from approximations to analogous physics of electromagnetic waves. Here, we present a gravitational form of the electromagnetic Chu limit that sets bounds on the achievable Q (quality factor) relating the ratio of stored energy to radiated energy in the underlying fields. In particular, we answer two fundamental physics questions: 1) what is the theoretical Q for gravitational quadrupole radiation sources, and 2) can gravitational Q be observed from recent measured astronomical data? Gravitational Q is shown to follow an inverse seventh-order power law, and gravitational-wave data is used to find observed values of Q for GW170817. Inasmuch as electromagnetic Q serves a central role in design and analysis of electrically-small antennas, the proposed gravitationalQ offers the potential for a similar utility in the design and analysis of gravitationally-small detectors and quadrupoles.