Parareal is a well-studied algorithm for numerically integrating systems of time-dependent differential equations by parallelising the temporal domain. Given some initial values at each temporal sub-interval, the algorithm iteratively locates a solution in a fixed number of iterations using a predictor-corrector, stopping once a tolerance is met. This iterative process combines solutions located by inexpensive (coarse resolution) and expensive (fine resolution) numerical integrators. In this paper, we introduce a \\\\textit{stochastic parareal} algorithm with the aim of accelerating the convergence of the deterministic parareal algorithm. Instead of providing the predictor-corrector with a deterministically located set of initial values, the stochastic algorithm samples initial values from dynamically varying probability distributions in each temporal sub-interval. The samples are then propagated in each sub-interval by the numerical method in parallel with the set of initial values yielding the most continuous (smoothest) trajectory across consecutive sub-intervals chosen as a more accurate set of initial values. These values are fed into the predictor-corrector, converging in fewer iterations than the deterministic algorithm, with a given probability. The performance of the introduced stochastic parareal, implemented using various probability distributions, is illustrated on systems of ordinary differential equations. When the number of sampled initial values is large enough, we show that stochastic parareal converges almost certainly in fewer iterations than the deterministic version while maintaining solution accuracy.