The installation of smart meters enables the collection of massive fine-grained electricity consumption data and makes individual consumer level load forecasting possible. Compared to aggregated loads, load forecasting for individual consumers is prone to non-stationary and stochastic features. In this paper, a probabilistic load forecasting method for individual consumers is proposed to handle the variability and uncertainty of future load profiles. Specifically, a deep neural network, long short-term memory (LSTM), is used to model both the long-term and short-term dependencies within the load profiles. Pinball loss, instead of the mean square error (MSE), is used to guide the training of the parameters. In this way, traditional LSTM-based point forecasting is extended to probabilistic forecasting in the form of quantiles. Numerical experiments are conducted on an open dataset from Ireland. Forecasting for both residential and commercial consumers is tested. Results show that the proposed method has superior performance over traditional methods.