Scanning tunneling spectroscopy measurements conducted on epitaxially grown bilayers of half-metallic ferromagnetic La2/3Ca1/3MnO3 (LCMO) on superconducting (SC) (100)YBa2Cu3O7-delta (YBCO) reveal long-range penetration of superconducting order into the LCMO. This anomalous proximity effect manifests itself in the tunneling spectra measured on the LCMO layer as gaps and zero bias conductance peaks. Remarkably, these proximity-induced spectral features were observed for bilayers with LCMO thickness of up to 30 nm, an order of magnitude larger than the expected ferromagnetic coherence length in LCMO. We argue that this long-range proximity effect can be accounted for by the formation of spin triplet pairing at the LCMO side of the bilayer due to magnetic inhomogeneity at the interface or at domain walls. Possible symmetries of the induced order parameter are discussed.