It is shown that ion transport in the banana regime in tokamaks is reduced in the presence of a strong shear in the radial electric field E(r), as is often observed in the edge region. For simplicity, the ordering with rho(pi)\d 1n E(r)/dr\ much greater than 1 but c\E(r)\/B(p)upsilon(ti) < 1 is adopted. Here, rho(pi) is the ion poloidal gyroradius, B(p) is the poloidal magnetic field strength, upsilon(ti) is the ion thermal speed, and c is the speed of light. A kinetic transport theory similar to those for bumpy tori and stellarators is developed to show that the ion thermal conductivity chi-i is reduced by a factor of roughly S-3/2, where S = 1 - (rho(pi)d 1n E(r)/dr)(cE(r)/B(p)upsilon(ti)). The result reflects more than simple orbit squeezing: The fraction of trapped ions is also modified by S.