  We present ground-based and Hubble Space Telescope optical observations of
the X-ray flash (XRF) 020903, covering 300 days. The afterglow showed a very
rapid rise in the first day, followed by a relatively slow decay in the next
few days. There was a clear bump in the light curve after ~25 days, accompanied
by a drastic change in the spectral energy distribution. The light curve and
the spectral energy distribution are naturally interpreted as the emergence --
and subsequent decay -- of a supernova (SN), similar to SN 1998bw. At peak
luminosity, the SN is estimated to be 0.8 +/- 0.1 mag fainter than SN1998bw.
This argues in favor of the existence of a supernova associated with this X-ray
flash. A spectrum obtained 35 days after the burst shows emission lines from
the host galaxy. We use this spectrum to put an upper limit on the oxygen
abundance of the host at [O/H] < -0.6 dex. We also discuss a possible trend
between the softness of several bursts and the early behavior of the optical
afterglow, in the sense that XRFs and X-ray rich GRBs seem to have a plateau
phase or even a rising light curve. This can be naturally explained in models
where XRFs are similar to GRBs but seen off the jet axis.
