Photovoltaic (PV) power generation varies randomly and intermittently with respect to the weather. For a microgrid with PV sources, this fluctuation not only affects the necessary configuration of the energy-storage capacity chosen in microgrid planning and design but also influences the microgrid operation. Consequently, accurately forecasting the PV output is crucial. For the operation of a PV-dominated microgrid, a new method for very short-term (VST) forecasting based on the maximum Lyapunov exponent (MLE) is proposed. First, historical power-generation data are divided into three weather conditions: sunny, cloudy, and rainy days. Then, a PV output series for the different weather conditions is constructed, and the chaotic characteristic is verified by reconstructing an attractor graph and calculating the MLE. Finally, using the MLE method, the PV generation under different historical weather conditions is forecasted. The raw output time series are measured data from a demonstration system installed on the rooftop of Building 6 at Hangzhou Dianzi University, China. The forecasting accuracy is evaluated using several statistical metrics and compared with that of forecasts obtained via the widely used auto-regression approach. Comparing the forecasts indicates that the MLE-based method is statistically but not universally more accurate for VST forecasting.