  Within the Oseen-Frank theory we derive numerically exact solutions for
axisymmetric localized states in chiral liquid crystal layers with homeotropic
anchoring. These solutions describe recently observed two-dimensional skyrmions
in confinement-frustrated chiral nematics [P. J. Acherman et al. Phys. Rev. E
90, 012505 (2014)]. We stress that these solitonic states arise due to a
fundamental stabilization mechanism responsible for the formation of skyrmions
in cubic helimagnets and other noncentrosymmetric condensed-matter systems.
