Correlations of two charged identical kaons (KchKch) are measured in pp collisions at s√=7~TeV by the ALICE experiment at the Large Hadron Collider (LHC). One-dimensional KchKch correlation functions are constructed in three multiplicity and four transverse momentum ranges. The KchKch femtoscopic source parameters R and λ are extracted. The KchKch correlations show a slight increase of femtoscopic radii with increasing multiplicity and a slight decrease of radii with increasing transverse momentum. These trends are similar to the ones observed for ππ and K0sK0s correlations in pp and heavy-ion collisions. However at high multiplicities, there is an indication that the one-dimensional correlation radii for charged kaons are larger than those for pions in contrast to what was observed in heavy-ion collisions at RHIC.