Models widely used to assess atmospheric chemical-dispersion hazards for emergency response rely on Acute Emergency Guideline Level (AEGL) or similar concentration guidelines to map geographic areas potentially affected by corresponding levels of toxic severity. By ignoring substantial, random variability in concentration over both time and space, such standard methods routinely underestimate the size of potentially affected areas. Underestimation due to temporal fluctuation---applicable to chemicals like hydrogen cyanide (HCN) for which peak concentrations best predict acute toxicity---becomes magnified by spatial fluctuation, defined as heterogeneity in average concentration at each location relative to standard-method predictions. The combined impact of spatiotemporal fluctuation on size of assessed threat areas was studied using a new, stochastic assessment method calibrated to Joint Urban 2003 Oklahoma City field-tracer data. For a hypothetical 60-min urban release scenario involving HCN gas, the stochastic method predicted that lethal/severe effects could occur in areas 20 or more times larger than those predicted by standard dispersion-modeling methods. Similar bias that may pertain to large indoor environments merits investigation.