We present the discovery of a strongly phase-variable absorption feature in the X-ray spectrum of the nearby, thermally-emitting, isolated neutron star RX J0720.4-3125. The absorption line was detected performing detailed phase-resolved spectroscopy in 20 XMM-Newton observations, covering the period May 2000 - September 2012. The feature has an energy of ~750eV, an equivalent width of ~30eV, and it is significantly detected for only ~20% of the pulsar rotation. The absorption feature appears to be stable over the timespan covered by the observations. Given its strong dependence on the pulsar rotational phase and its narrow width, a plausible interpretation is in terms of resonant proton cyclotron absorption/scattering in a confined magnetic structure very close to the neutron star surface. The inferred field in such a magnetic loop is B_loop ~ 2 x 10^{14} G, a factor of ~7 higher than the surface dipolar magnetic field.
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