  It has recently been proposed that the large-scale bias of dark matter halos
depends sensitively on primordial non-Gaussianity of the local form. In this
paper we point out that the strong scale dependence of the non-Gaussian halo
bias imprints a distinct signature on the covariance of cluster counts. We find
that using the full covariance of cluster counts results in improvements on
constraints on the non-Gaussian parameter f_NL of three (one) orders of
magnitude relative to cluster counts (counts + clustering variance) constraints
alone. We forecast f_NL constraints for the upcoming Dark Energy Survey in the
presence of uncertainties in the mass-observable relation, halo bias, and
photometric redshifts. We find that the DES can yield constraints on
non-Gaussianity of sigma(f_NL) ~ 1-5 even for relatively conservative
assumptions regarding systematics. Excess of correlations of cluster counts on
scales of hundreds of megaparsecs would represent a smoking gun signature of
primordial non-Gaussianity of the local type.
