Spin scalar chiral ordering gives rise to nontrivial topological characters and peculiar transport properties. Here, we examine how quantum spin fluctuations affect the spin scalar chiral ordering in itinerant electron systems. We consider the Kondo lattice model on a triangular lattice and perform the linear spin wave analysis in Chern insulator phases with spin scalar chiral ordering obtained in the case that the localized spins are classical. We find that, although quantum fluctuation destabilizes the spin scalar chiral phase at 3/4 filling that originates from the perfect nesting of the Fermi surface, it retains the phase at 1/4 filling that is induced by an effective positive biquadratic interaction. The reduction in the ordered magnetic moment by zero-point quantum fluctuation is considerably smaller than those in spin-only systems. The results suggest that the Chern insulator at 1/4 filling remains robust under quantum fluctuations. © 2013 The Physical Society of Japan.