We use the Cottingham method to calculate the pion and kaon electromag
netic mass differences with as few model-dependent inputs as possible.
The constraints of chiral symmetry at low energy, QCD at high energy,
and experimental data in between are used in the dispersion relation.
We find excellent agreement with experiment for the pion mass differe
nce. The kaon mass difference exhibits a strong violation of the lowes
t order prediction of Dashen's theorem, in qualitative agreement with
several other recent calculations.