  We show theoretically that hot-electron nanobolometers consisting of a small
piece of normal metal, capacitively coupled to a superconducting antenna
through a pair of normal metal--insulator--superconductor (NIS) tunnel
junctions may be used as far-infrared photon counters. To make the device most
effective at high counting rates, we suggest the use of the bolometer in the
simplest configuration, when the NIS tunnel junctions are used as both an
electron cooler and thermometer. The absorption of the photon in the normal
metal produces a pulse in the electron temperature, which is measured by the
NIS junctions. The counter may resolve photons up to 0.3--0.4 mm wavelength and
has a typical re-equilibration time constant of about 20 ns.
