Human cortical organoids, three-dimensional neuronal cell cultures derived from human induced pluripotent stem cells, have recently emerged as promising models of human brain development and dysfunction. Transplantation of human brain organoids into the mouse brain has been shown to be a successful in vivo model providing vascularization for long term chronic experiments. However, chronic functional connectivity and responses evoked by external sensory stimuli has yet to be demonstrated, due to limitations of chronic recording technologies. Here, we develop an experimental paradigm based on transparent graphene microelectrode arrays and two-photon imaging for longitudinal, multimodal monitoring of human organoids transplanted in the mouse cortex. The transparency of graphene microelectrodes permits visual and optical inspection of the transplanted organoid and the surrounding cortex throughout the chronic experiments where local field potentials and multi-unit activity (MUA) are recorded during spontaneous activity and visual stimuli. These experiments reveal that visual stimuli evoke electrophysiological responses in the organoid, matching the responses from the surrounding cortex. Increases in the power of the gamma and MUA bands as well as phase locking of MUA events to slow oscillations evoked by visual stimuli suggest functional connectivity established between the human and mouse tissue. Optical imaging through the transparent microelectrodes shows vascularization of the organoids. Postmortem histological analysis exhibits morphological integration and synaptic connectivity with surrounding mouse cortex as well as migration of organoid cells into the surrounding cortex. This novel combination of stem cell and neural recording technologies could serve as a unique platform for comprehensive evaluation of organoids as models of brain development and dysfunction and as personalized neural prosthetics to restore lost, degenerated, or damaged brain regions.