We construct a mixed analog/digital switched-capacitor (SC) chaotic neuro-computer prototype with 400 neurons and 160000 synapses. We observe a chaotic search dynamics arises from chaotic itinerancy from the prototype system. Especially, we first implement a dynamical associative memory on the system. Then, we apply the chaotic search dynamics to solve the quadratic assignment problem, which is one of the NP-hard combinatorial optimization problems. The chaotic search dynamics depends heavily on the complexity in real number. The analog SC chaotic neurons used in this study can handle real numbers through their continuous variables, and therefore they would faithfully and naturally reproduce the chaotic search behavior.