There is great controversy whether the carcinogenicity of chemicals is dose-dependent and whether a "threshold" dose exists below which cancer will not be induced by exposure. Evidence for dose-dependency exists and is believed to be accepted generally if extricated as it should be from the "threshold" concept. The "threshold" concept conflict is not likely to be resolved in the foreseeable future; proponents and opponents argue their case in a manner similar to those arguing religion. In this paper the various arguments are reviewed. Subsequently, a chemical process model for carcinogenesis is developed based on the generally accepted evidence that the carcinogenic activity of many chemicals can be related to electrophilic alkylation of DNA. Using this model, some incidence of cancer, albeit negligible, will be predicted regardless how low the dose. However, the model reveals that the incidence of cancer induced by real-life exposures is likely to be greatly overestimated by currently used stochastic statistical extrapolations. Even more important, modeling of the chemical processes involved in the fate of a carcinogenic chemical in the body reveals experimental approaches to elucidating the mechanism(s) of carcinogenesis and ultimately a more scientifically sound basis for assessing the hazard of low-level exposure to a chemical carcinogen.