We present a measurement of the ratio of the tt production cross section via gluon-gluon fusion to the total tt production cross section in pp collisions at s√=1.96  TeV at the Tevatron. Using a data sample with an integrated luminosity of 955  pb−1 recorded by the CDF II detector at Fermilab, we select events based on the tt decay to lepton+jets. Using an artificial neural network technique we discriminate between tt events produced via qq annihilation and gg fusion, and find Gf=σ(gg→tt)/σ(pp→tt)<0.33 at the 68% confidence level. This result is combined with a previous measurement to obtain the most stringent measurement of this quantity by CDF to date, Gf=0.07+0.15−0.07.