The Tau-Leap strategy for stochastic simulations of chemical reaction systems due to Gillespie and co-workers has had considerable impact on various applications. This strategy is reexamined with Chebyshevs inequality for random variables as it provides a rigorous probabilistic basis for a measured tau-leap thus adding significantly to simulation efficiency. It is also shown that existing strategies for simulation times have no probabilistic assurance that they satisfy the tau-leap criterion while the use of Chebyshevs inequality leads to a specified degree of certainty with which the tau-leap criterion is satisfied. This reduces the loss of sample paths which do not comply with the tau-leap criterion. The performance of the present algorithm is assessed, with respect to one discussed by Cao et al. (J. Chem. Phys. 2006, 124, 044109), a second pertaining to binomial leap (Tian and Burrage J. Chem. Phys. 2004, 121, 10356; Chatterjee et al. J. Chem. Phys. 2005, 122, 024112; Peng et al. J. Chem. Phys. 2007, 126, 224109), and a third regarding the midpoint Poisson leap (Peng et al., 2007; Gillespie J. Chem. Phys. 2001, 115, 1716). The performance assessment is made by estimating the error in the histogram measured against that obtained with the so-called stochastic simulation algorithm. It is shown that the current algorithm displays notably less histogram error than its predecessor for a fixed computation time and, conversely, less computation time for a fixed accuracy. This computational advantage is an asset in repetitive calculations essential for modeling stochastic systems. The importance of stochastic simulations is derived from diverse areas of application in physical and biological sciences, process systems, and economics, etc. Computational improvements such as those reported herein are therefore of considerable significance.