We present observations of SCP 06F6, an unusual optical transient discovered during the Hubble Space Telescope Cluster Supernova Survey. The transient brightened over a period of ~100 days, reached a peak magnitude of ~21.0 in both i_775_ and z_850_, and then declined over a similar timescale. There is no host galaxy or progenitor star detected at the location of the transient to a 3{sigma} upper limit of i_775_>=26.4 and z_850_>=26.1, giving a corresponding lower limit on the flux increase of a factor of ~120. Multiple spectra show five broad absorption bands between 4100{AA} and 6500{AA}, and a mostly featureless continuum longward of 6500{AA}. The shape of the light curve is inconsistent with microlensing. The transient's spectrum, in addition to being inconsistent with all known supernova types, does not match any spectrum in the Sloan Digital Sky Survey database. We suggest that the transient may be one of a new class.