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 5kpc 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 Fjorm stream by Ibata et al (2019ApJ...872..152I). 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.