MIDIS: MIRI uncovers Virgil, the first Little Red Dot with clear detection of its host galaxy at z ~ 6.6

We present Virgil, a MIRI extremely red object (MERO) detected with the F1000W filter as part of the MIRI Deep Imaging Survey (MIDIS) observations of the Hubble Ultra Deep Field (HUDF). Virgil is a Lyman-$\alpha$ emitter (LAE) at $z_{spec} = 6.6312\pm 0.0019$ (from VLT/MUSE) with a rest-frame UV-to-optical spectral energy distribution (SED) typical of LAEs at similar redshifts. However, MIRI observations reveal an unexpected extremely red color at rest-frame near-infrared wavelengths, $\rm F444W - F1000W = 2.33 \pm 0.06$. Such steep rise in the near-infrared, completely missed without MIRI imaging, is poorly reproduced by models including only stellar populations and hints towards the presence of an Active Galactic Nucleus (AGN). According to the shape of its overall SED, Virgil belongs to the recently discovered population of Little Red Dots (LRDs) but displays an extended rest-frame UV-optical wavelengths morphology following a 2D-S\'ersic profile with average index $n = 0.93^{+0.85}_{-0.31}$ and $r_e = 0.49^{+0.05}_{-0.11}$ pkpc. Only at MIRI wavelengths Virgil is unresolved due to the coarser PSF. We also estimate a bolometric luminosity $L_{\rm bol, AGN} = (8.9-11)\times 10^{44}\rm~erg~s^{-1}$ and a supermassive black hole mass $M_{\rm BH} = (7-9)\times 10^6\rm ~ M_\odot$ (if $\lambda_{\rm Edd} = 1$) in agreement with recently reported values for LRDs. This discovery demonstrates the crucial importance of deep MIRI surveys to find AGN amongst high-$z$ galaxies that otherwise would be completely missed and raises the question of how common Virgil-like objects could be in the early Universe.