Renormalized statistical equations which characterize a long wavelength resistive tearing mode when the magnetic field is stochastic are derived. The theory predicts a broadening of the current layer of the mode due to enhanced perpendicular electron motion. This increase in the current layer width is significant for fluctuation levels 〈(δB/B)2〉 as small as 10−8, where 〈(δB/B)2〉 is the ratio of the energy in the magnetic fluctuations to the equilibrium magnetic energy. As a consequence of this broadening, the transition from exponential to algebraic growth is not attained until the magnetic energy density of the mode exceeds the total magnetic energy density of all the other fluctuations.