TESS Hunt for Young and Maturing Exoplanets (THYME) VI: an 11 Myr giant planet transiting a very low-mass star in Lower Centaurus Crux

Mature super-Earths and sub-Neptunes are predicted to be $\simeq$Jovian radius when younger than 10 Myr. Thus, we expect to find 5-15$R_\oplus$ planets around young stars even if their older counterparts harbor none. We report the discovery and validation of TOI 1227 b, a $0.85\pm0.05 R_J$ (9.5$R_\oplus$) planet transiting a very low-mass star ($0.170\pm0.015 M_\odot$) every 27.4 days. TOI 1227's kinematics and strong lithium absorption confirm it is a member of a previously discovered sub-group in the Lower Centaurus Crux OB association, which we designate the Musca group. We derive an age of 11$\pm$2 Myr for Musca, based on lithium, rotation, and the color-magnitude diagram of Musca members. The TESS data and ground-based followup show a deep (2.5%) transit. We use multiwavelength transit observations and radial velocities from the IGRINS spectrograph to validate the signal as planetary in nature, and we obtain an upper limit on the planet mass of $\simeq0.5 M_J$. Because such large planets are exceptionally rare around mature low-mass stars, we suggest that TOI 1227 b is still contracting and will eventually turn into one of the more common $<5R_\oplus$ planets.