  We present pulse phase-resolved X-ray spectra of the high mass X-ray binary
Vela X-1 using the Rossi X-ray Timing Explorer. We observed Vela X-1 in 1998
and 2000 with a total observation time of ~90 ksec. We find an absorption
feature at 23.3 +1.3 -0.6 kev in the main pulse, that we interpret as the
fundamental cyclotron resonant scattering feature (CRSF). The feature is
deepest in the rise of the main pulse where it has a width of 7.6 +4.4 -2.2 kev
and an optical depth of 0.33 +0.06 -0.13. This CRSF is also clearly detected in
the secondary pulse, but it is far less significant or undetected during the
pulse minima. We conclude that the well known CRSF at 50.9 +0.6 -0.7 kev, which
is clearly visible even in phase-averaged spectra, is the first harmonic and
not the fundamental. Thus we infer a magnetic field strength of B=2.6 x 10^12
G.
