Bose-Einstein correlations of charged kaons were measured near mid-rapidityin central Pb+Pb collisions at 158 A·GeV by the NA49 experiment at theCERN SPS. Source radii were extracted using the Yano-Koonin-Podgoretsky andBertsch-Pratt parameterizations. The results are compared to published piondata. The measured m_⊥ dependence for kaons and pions is consistent withcollective transverse expansion of the source and a freeze-out time of about9.5 fm.