We have successfully interfaced living neuronal networks with a defined geometry of synaptic connections to a semiconductor chip, enabling a non-invasive supervision of network activity at a single-cell level. Two networks of two and four neurons are presented and the signaling pathways are discussed. The outgrowth of neurons from the pond snail Lymnaea stagnalis and the formation of synapses are controlled by topographical structures processed from a polyester resist. Action potentials are evoked in individual neurons by capacitive stimulators integrated in the chip. They propagate along guided neurites, pass through electrical synapses, and trigger postsynaptic excitations that are recorded by field-effect transistors. The networks represent proof-of-principle experiments for the development of complex hybrid neuroelectronic devices for applications in brain research, pharmacology, and information technology.