By taking advantage of large changes in geometric and electronic structure during the reversible trans-cis isomerisation, azobenzene derivatives have been widely studied for potential applications in information processing and digital storage devices. Here we report an unusual discovery of unambiguous conductance switching upon light and electric field-induced isomerisation of azobenzene in a robust single-molecule electronic device for the first time. Both experimental and theoretical data consistently demonstrate that the azobenzene sidegroup serves as a viable chemical gate controlled by electric field, which efficiently modulates the energy difference of trans and cis forms as well as the energy barrier of isomerisation. In conjunction with photoinduced switching at low biases, these results afford a chemically-gateable, fully-reversible, two-mode, single-molecule transistor, offering a fresh perspective for creating future multifunctional single-molecule optoelectronic devices in a practical way.