Chile has become one of the countries most affected by COVID-19, a pandemic that has generated a large number of cases worldwide. If not detected and treated in time, COVID-19 can cause multi-organ failure and even death. Therefore, it is necessary to understand the behavior of the spread of COVID-19 as well as the projection of infections and deaths. This information is very relevant so that public health organizations can distribute financial resources efficiently and take appropriate containment measures. In this research, we compare different time series methodologies to predict the number of confirmed cases of and deaths from COVID-19 in Chile. The methodology used in this research consisted of modeling cases of both confirmed diagnoses and deaths from COVID-19 in Chile using Autoregressive Integrated Moving Average (ARIMA henceforth) models, Exponential Smoothing techniques, and Poisson models for time-dependent count data. Additionally, we evaluated the accuracy of the predictions using a training set and a test set. The dataset used in this research indicated that the most appropriate model is the ARIMA time series model for predicting the number of confirmed COVID-19 cases, whereas for predicting the number of deaths from COVID-19 in Chile, the most suitable approach is the damped trend method. The ARIMA models are an alternative to modeling the behavior of the spread of COVID-19; however, depending on the characteristics of the dataset, other methodologies can better predict the behavior of these records, for example, the Holt-Winter method implemented with time-dependent count data.