The basic reproductive ratio, R0, is a central quantity in the investigation and management of infectious pathogens. The standard model for describing stochastic epidemics is the continuous time epidemic birth-and-death process. The incidence data used to fit this model tend to be collected in discrete units (days, weeks, etc.), which makes model fitting, and estimation of R0 difficult. Discrete time epidemic models better match the time scale of data collection but make simplistic assumptions about the stochastic epidemic process. By investigating the nature of the assumptions of a discrete time epidemic model, we derive a bias corrected maximum likelihood estimate of R0 based on the chain binomial model. The resulting 'removal' estimators provide estimates of R0 and the initial susceptible population size from time series of infectious case counts. We illustrate the performance of the estimators on both simulated data and real epidemics. Lastly, we discuss methods to address data collected with observation error.