Lightning is responsible for the most area annually burned by wildfires in the extratropical region of the Northern Hemisphere. Hence, predicting the occurrence of wildfires requires reliable forecasting of the chance of cloud-to-ground lightning strikes during storms. Here, we describe the development and verification of a probabilistic lightning-strike algorithm running on a uniform 20 km grid over the continental USA and Alaska. This is the first and only high-resolution lightning forecasting model for North America derived from 29-year-long data records. The algorithm consists of a large set of regional logistic equations parameterized on the long-term data records of observed lightning strikes and meteorological reanalysis fields from NOAA. Principal Component Analysis was employed to extract 13 principal components from a list of 611 potential predictors. Our analysis revealed that the occurrence of cloud-to-ground lightning strikes primarily depends on three factors: the temperature and geopotential heights across vertical pressure levels, the amount of low-level atmospheric moisture, and wind vectors. These physical variables isolate the conditions that are favorable for the development of thunderstorms and impact the vertical separation of electric charges in the lower troposphere during storms, which causes the voltage potential between the ground and the cloud deck to increase to a level that triggers electrical discharges. The results from a forecast verification using independent data showed excellent model performance, thus making this algorithm suitable for incorporation into models designed to forecast the chance of wildfire ignitions.