To date, 14 high-redshift (z>1.0) galaxy clusters with mass measurements have been observed, spectroscopically confirmed, and are reported in the literature. These objects should be exceedingly rare in the standard Λ cold dark matter (ΛCDM) model. We conservatively approximate the selection functions of these clusters' parent surveys and quantify the tension between the abundances of massive clusters as predicted by the standard ΛCDM model and the observed ones. We alleviate the tension, considering non-Gaussian primordial perturbations of the local type, characterized by the parameter fNL, and derive constraints on fNL arising from the mere existence of these clusters. At the 95% confidence level, fNL>467, with cosmological parameters fixed to their most likely WMAP5 values, or fNL≳123 (at 95% confidence) if we marginalize over prior WMAP5 parameters. In combination with fNL constraints from cosmic microwave background and halo bias, this determination implies a scale dependence of fNL at ≃3σ. Given the assumptions made in the analysis, we expect any future improvements to the modeling of the non-Gaussian mass function, survey volumes, or selection functions to increase the significance of fNL>0 found here. In order to reconcile these massive, high-z clusters with fNL=0, their masses would need to be systematically lowered by 1.5σ, or the σ8 parameter should be ∼3σ higher than cosmic microwave background (and large-scale structure) constraints. The existence of these objects is a puzzle: it either represents a challenge to the ΛCDM paradigm or it is an indication that the mass estimates of clusters are dramatically more uncertain than we think.