We obtained observations of GRB 080319B (GCN 7427) with HST/WFPC2 in F606W and F814W filters on 2008 April 7th (2 orbits in each filter).
These data show the fading afterglow at magnitude F(814W_AB)=24.2 and F(606W_AB)=24.5. This fading is consistent within the errors with a continued power-law decline in optical brightness.
PSF subtraction reveals no obvious sign of an underlying host galaxy, although there is what appears to be a separate galaxy 1.5 arcsec to the south, which might be producing one of the foreground absorption systems (GCN 7451).
Further analysis is ongoing.