The Hedgehog (Hh) signaling pathway is integral for embryonic development and normal cell maintenance. However, aberrant expression of the Hh pathway is recognized as the oncogenic driving force for basal cell carcinoma (BCC). Current chemotherapeutic treatments that inhibit Hh signaling allow treatment of only locally advanced and metastatic BCCs via inhibition of the transmembrane protein, smoothened. It is further recognized that downstream mutations often lead to chemoresistant tumor recurrence. The Gli proteins are the ultimate regulators of Hh signaling and belong to a family of Cys2His2 zinc finger transcription factors (ZnFTFs) that we have shown can be irreversibly inhibited by a series of cobalt(III) Schiff base-DNA (CoSB-DNA) conjugates. However, a significant challenge is the delivery of CoSB-DNA complexes in mammalian tissues. Herein, we report a polyethyleneimine-functionalized graphene oxide nanoconjugate (GOPEI) that delivers CoGli, a CoSB-DNA complex that targets Gli specifically. We describe the characterization of the surface functionalization of GOPEI and accumulation in ASZ murine BCC cells via confocal microscopy and inductively coupled plasma-mass spectrometry (ICP-MS). Lysosomal escape of CoGli is further confirmed by confocal microscopy. We report the successful targeting of Gli by CoGli and a 17-fold improvement in potency over small-molecule Gli inhibitor GANT-61 in inhibiting Hh-driven migration of ASZ murine BCC cells. This study provides a promising starting point for further investigating CoGli inhibitors of Hh signaling in developed mammalian tissues.