A method to calculate the electron Landau damping of toroidal Alfven eigenrnodes (TAE) is presented. Due to the presence of a small current produced by thermal electrons near the trapped-passing boundary, a jump in the electrostatic potential near the k|| = 0 surface occurs. An analytic expression for this jump is derived in the low-β. large-aspect-ratio limit. and is suitable for incorporation into either numerical eigenvalue codes or analytic models. In the limit of small magnetic shear, the calculation is carried through analytically giving a simple local expression for the damping.