We present efforts in the fields of machine learning and time series forecasting to accurately predict counts of future suspected opioid overdoses recorded by Emergency Medical Services (EMS) in the state of Kentucky. Forecasts help government agencies properly prepare and distribute resources related to opioid overdoses. Our approach uses county and district level aggregations of suspected opioid overdose encounters and forecasts future counts for different time intervals. Models with different levels of complexity were evaluated to minimize forecasting error. A variety of additional covariates relevant to opioid overdoses and public health were tested to determine their impact on model performance. Our evaluation shows that useful predictions can be generated with limited error for different types of regions, and high performance can be achieved using commonly available covariates and relatively simple forecasting models.