We present spectra of the optical transient (OT) associated with GRB 021004. The spectra show a blue continuum with superposed absorption features and one emission line. We confirm two intervening metal-line systems at z = 1.380 and z = 1.602 and one very strong absorption system at a redshift of z = 2.323. Ly_alpha emission is also seen at this redshift. While the spectrum of the OT overall cannot be simply described with a power law, the spectral index over the range 5500-8850 A is steep, F_nu ~ nu^(-0.96 +/- 0.03). Comparison of spectra from multiple epochs shows a distinct color evolution with the OT becoming redder with time over the first three days. This is the first clear example of color change in an OT detected spectroscopically.