We present a measurement of the top quark mass in the all hadronic channel (tt→bbq1q2q3q4) using 943  pb−1 of pp collisions at s√=1.96  TeV collected at the CDF II detector at Fermilab (CDF). We apply the standard model production and decay matrix element (ME) to tt¯ candidate events. We calculate per-event probability densities according to the ME calculation and construct template models of signal and background. The scale of the jet energy is calibrated using additional templates formed with the invariant mass of pairs of jets. These templates form an overall likelihood function that depends on the top quark mass and on the jet energy scale (JES). We estimate both by maximizing this function. Given 72 observed events, we measure a top quark mass of 171.1±3.7(stat+JES)±2.1(syst)  GeV/c2. The combined uncertainty on the top quark mass is 4.3  GeV/c2.