  $\epsilon$ Eridani is the closest star to our Sun known to host a debris
disc. Prior observations in the (sub-)millimetre regime have potentially
detected clumpy structure in the disc and attributed this to interactions with
an (as yet) undetected planet. However, the prior observations were unable to
distinguish between structure in the disc and background confusion. Here we
present the first ALMA image of the entire disc, which has a resolution of
1.6"$\times$1.2". We clearly detect the star, the main belt and two point
sources. The resolution and sensitivity of this data allow us to clearly
distinguish background galaxies (that show up as point sources) from the disc
emission. We show that the two point sources are consistent with background
galaxies. After taking account of these, we find that resolved residuals are
still present in the main belt, including two clumps with a $>3\sigma$
significance -- one to the east of the star and the other to the northwest. We
perform $n$-body simulations to demonstrate that a migrating planet can form
structures similar to those observed by trapping planetesimals in resonances.
We find that the observed features can be reproduced by a migrating planet
trapping planetesimals in the 2:1 mean motion resonance and the symmetry of the
most prominent clumps means that the planet should have a position angle of
either ${\sim10^\circ}$ or ${\sim190^\circ}$. Observations over multiple epochs
are necessary to test whether the observed features rotate around the star.
