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We present the first measurement of event-by-event fluctuations in the kaon sector in Pb – Pb collisions at √sNN = 2.76 TeV with the ALICE detector at the LHC. The robust fluctuation correlator νdyn is used to evaluate the magnitude of fluctuations of the relative yields of neutral and charged kaons, as well as the relative yields of charged kaons, as a function of collision centrality and selected kinematic ranges. While the correlator νdyn[K+,K−] exhibits a scaling approximately in inverse proportion of the charged particle multiplicity, νdyn[K0 S ,K±] features a significant deviation from such scaling. Within uncertainties, the value of νdyn[K0 S ,K±] is independent of the selected transverse momentum interval, while it exhibits a pseudorapidity dependence. The results are compared with HIJING, AMPT and EPOS–LHC predictions, and are further discussed in the context of the possible production of disoriented chiral condensates in central Pb – Pb collisions.