The first successful quantitative account of the electron thermal conductivity χe in a tokamak experiment due to imperfect magnetic surfaces is presented. The unstable spectrum of microtearing instabilities is calculated with the GS2 code for a well-behaved H-mode plasma in the National Spherical Tokamak Experiment [M. Ono et al., Nucl. Fusion 40, 557 (2000)], with 6 MW deuterium neutral beam heating at Ip=0.75MA, Bt=0.5T. The application of existing nonlinear theory shows that the unstable modes can produce overlapping magnetic islands leading to global stochastic magnetic fields. The calculated χe based on the present theory is in reasonable agreement with the values from transport analysis of the experimental data over the entire region (0.4<r∕a<0.75) where the electron temperature gradient is strong enough to make microtearing the most unstable mode. There is no adjustable parameter in this comparison. This instability can be avoided by reversed magnetic shear or by heating the electrons to lower the electron-ion collision frequency.