Deciding between the use of market orders and limit orders is an important question in practical optimal trading problems. A key ingredient in making this decision is understanding the uncertainty of the execution of a limit order, that is, the fill probability or the probability that an order will be executed within a certain time horizon. Equivalently, one can estimate the distribution of the time-to-fill. We propose a data-driven approach based on a recurrent neural network to estimate the distribution of time-to-fill for a limit order conditional on the current market conditions. Using a historical data set, we demonstrate the superiority of this approach to several benchmark techniques. This approach also leads to significant cost reductions while implementing a trading strategy in a prototypical trading problem.