  A method to search for tidal streams and to fit their orbits based on maximum
likelihood is presented and applied to the Gaia data. Tests of the method are
performed showing how a simulated stream produced by tidal stripping of a star
cluster is recovered when added to a simulation of the Gaia catalogue. The
method can be applied to search for streams associated with known progenitors
or to do blind searches in a general catalogue. As the first example, we apply
the method to the globular cluster M68 and detect its clear tidal stream
stretching over the whole North Galactic hemisphere, and passing within 5 kpc
of the Sun. This is one of the closest tidal streams to us detected so far, and
is highly promising to provide new constraints on the Milky Way gravitational
potential, for which we present preliminary fits finding a slightly oblate dark
halo consistent with other observations. We identify the M68 tidal stream with
the previously discovered Fj\"orm stream by Ibata et al. The tidal stream is
confirmed to contain stars that are consistent with the HR-diagram of M68. We
provide a list of 115 stars that are most likely to be stream members, and
should be prime targets for follow-up spectroscopic studies.
