  In this article we introduce a generalization of locally conformally Kaehler
metrics from complex manifolds to complex analytic spaces with singularities
and study which properties of locally conformally Kaehler manifolds still hold
in this new setting. We prove that if a complex analytic space has only
quotient singularities, then it admits a locally conformally Kaehler metric if
and only if its universal cover admits a Kaehler metric such that the deck
automorphisms act by homotheties of the Kaehler metric. We also prove that the
blow-up at a point of a LCK complex space is also LCK.
