  It may be unsurprising that the most common approach to finding
proto-clusters is to search for over-densities of galaxies. Upgrades to
submillimetre (submm) interferometers and the advent of the James Webb Space
Telescope will soon offer the opportunity to find more distant candidate
proto-clusters in deep sky surveys without any spectroscopic confirmation. In
this letter, we report the serendipitous discovery of an extremely dense region
centred on the blazar, J0217-0820, at z=0.6 in the ALMACAL sky survey. Its
density is eight times higher than that predicted by blind submm surveys. Among
the seven submm-bright galaxies, three are as bright as conventional
single-dish submm galaxies, with S_870um > 3mJy. The over-density is thus
comparable to the densest known and confirmed proto-cluster cores. However,
their spectra betray a wide range of redshifts. We investigate the likelihood
of line-of-sight projection effects using light cones from cosmological
simulations, finding that the deeper we search, the higher the chance that we
will suffer from such projection effects. The extreme over-density around
J0217-0820 demonstrates the strong cosmic variance we may encounter in the deep
submm surveys. Thus, we should also question the fidelity of galaxy
proto-cluster candidates selected via over-densities of galaxies, where the
negative K correction eases the detection of dusty galaxies along an
extraordinarily extended line of sight.
