The gravitomagnetic monopole is the proposed gravitational analogue of
Dirac's magnetic monopole, and if detected, a new area of fundamental physics
will be opened. Here we find the first observational evidence of such a
monopole in the following way. Three primary methods to measure the black hole
spin, based on the relativistic precession model of quasi-periodic oscillations
in X-rays, broad relativistic X-ray spectral line and X-ray continuum spectrum,
give significantly different spin values for the accreting black hole in GRO
J1655--40. We demonstrate that the inclusion of just one additional parameter,
that is the so-called NUT parameter or the gravitomagnetic monopole, can not
only make the spin and other parameter values inferred from these three
independent methods consistent with each other, but also make the inferred
black hole mass consistent with an independently measured mass value. We argue
that this evidence of the gravitomagnetic monopole in nature is not a result of
fine-tuning, and hence is robust within our paradigm. Finally, our results
tentatively suggest that the collapsed object in GRO J1655--40 could be a naked
singularity.