A computational technique is described and demonstrated that can decrease by three orders of magnitude the computer time required to treat detailed chemistry in reactive flow calculations. The method is based on the in situ adaptive tabulation (ISAT) of the accessed region of the composition space - the adaptation being to control the tabulation errors. Test calculations are performed for non-premixed methane - air combustion in a statistically-homogeneous turbulent reactor, using a kinetic mechanism with 16 species and 41 reactions. The results show excellent control of the tabulation errors with respect to a specified error tolerance; and a speed-up factor of about 1000 is obtained compared to the direct approach of numerically integrating the reaction equations. In the context of PDF methods, the ISAT technique makes feasible the use of detailed kinetic mechanisms in calculations of turbulent combustion. The technique can also be used with reduced mechanisms, and in other approaches for calculating reactive flows (e.g. finite difference methods).