  The phase diagram of hole-doped copper oxides shows four different electronic
phases existing at zero temperature. Familiar among these are the Mott
insulator, high-transition-temperature superconductor and metallic phases. A
fourth phase, ofunknown identity, occurs at light doping along the
zero-temperature bound of the `pseudogap' regime. This regime is rich in
peculiar electronic phenomena, prompting numerous proposals that it contains
some form of hidden electronic order. Here we present low-temperature
electronic structure imaging studies of a lightly hole-doped copper oxide:
Ca_{2-x}Na_{x}CuO_{2}Cl_{2}. Tunnelling spectroscopy (at energies |E|>100 meV)
reveals electron extraction probabilities greatly exceeding those for
injection, as anticipated for a doped Mott insulator. However, for |E|<100 meV,
the spectrum exhibits a V-shaped energy gap centred on E=0. States within this
gap undergo intense spatial modulations, with the spatial correlations of a
four CuO_{2}-unit-cell square checkerboard, independent of energy. Intricate
atomic-scale electronic structure variations also exist within the
checkerboard. These data are consistent with an unanticipated crystalline
electronic state, possibly the hidden electronic order, existing in the
zero-temperature pseudogap regime of Ca_{2-x}Na_{x}CuO_{2}Cl_{2}.
