  Classical novae commonly show evidence of rapid dust formation within months
of the outburst. However, it is unclear how molecules and grains are able to
condense within the ejecta, given the potentially harsh environment created by
ionizing radiation from the white dwarf. Motivated by the evidence for powerful
radiative shocks within nova outflows, we propose that dust formation occurs
within the cool, dense shell behind these shocks. We incorporate a simple
molecular chemistry network and classical nucleation theory with a model for
the thermodynamic evolution of the post-shock gas, in order to demonstrate the
formation of both carbon and forsterite ($\rm Mg_2SiO_4$) grains. The high
densities due to radiative shock compression ($n \sim 10^{14}$ cm$^{-3}$)
result in CO saturation and rapid dust nucleation. Grains grow efficiently to
large sizes $\gtrsim 0.1\mu$m, in agreement with IR observations of
dust-producing novae, and with total dust masses sufficient to explain massive
extinction events such as V705 Cas. As in dense stellar winds, dust formation
is CO-regulated, with carbon-rich flows producing carbon-rich grains and
oxygen-rich flows primarily forming silicates. CO is destroyed by non-thermal
particles accelerated at the shock, allowing additional grain formation at late
times, but the efficiency of this process appears to be low. Given observations
showing that individual novae produce both carbonaceous and silicate grains, we
concur with previous works attributing this bimodality to chemical
heterogeneity of the ejecta. Nova outflows are diverse and inhomogeneous, and
the observed variety of dust formation events can be reconciled by different
abundances, the range of shock properties, and the observer viewing angle. The
latter may govern the magnitude of extinction, with the deepest extinction
events occurring for observers within the binary equatorial plane.
