A new type of individual-cell-based on-chip multielectrode array (MEA) cell-cultivation system with an agarose microchamber (AMC) array for topographical control of the network patterns of a living neuronal network has been developed. The advantages of this system are that it allows control of the cell positions and numbers for cultivation using AMCs, as well as easy and flexible control of the pattern of connections between the AMCs through photothermal etching where a portion of the agarose layer is melted with a 1480 nm infrared laser beam. With adequate laser power, narrow micrometer-order grooves (microchannels) can easily be fabricated that can be used to combine neighbouring AMCs to enable topographical control of the neural network pattern. Using this system, an individual-cell-based neural network pattern was formed of rat hippocampal cells within the AMC array without cells escaping from the electrode positions in the microchamber during an eight-day cultivation, and could record cell firing in response to 1.5 V, 500 kHz stimulation through an electrode. This demonstrated the potential of the on-chip AMCMEA cell cultivation system for long-term single-cell-based electrophysiological measurement of a neural network system.