  We present detailed submillimeter- through centimeter-wave observations of
the extraordinary extragalactic transient AT2018cow. The apparent
characteristics -- the high radio luminosity, the long-lived emission plateau
at millimeter bands, and the sub-relativistic velocity -- have no precedent. A
basic interpretation of the data suggests $E_k \gtrsim 10^{48}$ erg coupled to
a fast but sub-relativistic ($v \approx 0.13c$) shock in a dense ($n_e \approx
3 \times 10^{5}\,$cm$^{-3}$) medium. We find that the X-ray emission is not
naturally explained by an extension of the radio-submm synchrotron spectrum,
nor by inverse Compton scattering of the dominant blackbody UVOIR photons by
energetic electrons within the forward shock. By $\Delta t \approx20\,$days,
the X-ray emission shows spectral softening and erratic inter-day variability.
Taken together, we are led to invoke an additional source of X-ray emission:
the central engine of the event. Regardless of the nature of this central
engine, this source heralds a new class of energetic transients shocking a
dense medium, which at early times are most readily observed at millimeter
wavelengths.
