  We report the discovery of a pair of extremely reddened classical Cepheid
variable stars located in the Galactic plane behind the bulge, using
near-infrared time-series photometry from the VVV Survey. This is the first
time that such objects have ever been found in the opposite side of the
Galactic plane. The Cepheids have almost identical periods, apparent
brightnesses and colors. From the near-infrared Leavitt law, we determine their
distances with ~1.5% precision and ~8% accuracy. We find that they have a same
total extinction of A(V)~32 mag, and are located at the same heliocentric
distance of <d>=11.4+/-0.9 kpc, and less than 1 pc from the true Galactic
plane. Their similar periods indicate that the Cepheids are also coeval, with
an age of ~48+/-3 Myr, according to theoretical models. They are separated by
an angular distance of only 18.3", corresponding to a projected separation of
~1 pc. Their position coincides with the expected location of the Far 3 kpc Arm
behind the bulge. Such a tight pair of similar classical Cepheids indicates the
presence of an underlying young open cluster, that is both hidden behind heavy
extinction and disguised by the dense stellar field of the bulge. All our
attempts to directly detect this "invisible cluster" have failed, and deeper
observations are needed.
