Previous studies have demonstrated the electropermeabilization of cell membranes exposed to an electric field with moderate intensity (<2 V/cm) and a frequency of <100 MHz. Bioimpedance spectroscopy (BIS) is an electrical characterization technique that can be useful in studying this phenomenon because it is already used for electroporation. In this paper, we report a device designed to perform BIS on single cells and expose them to an electric field simultaneously. It also allows cells to be monitored by visualization through a transparent exposure electrode. This device is based on a lab-on-a-chip (LOC) with a microfluidic cell-trapping system and microelectrodes for BIS characterization. We present numerical simulations that support the design of the LOC. We also describe the fabrication of the LOC and the first electrical characterization of its measurement bandwidth. This first test, performed on reference medium with a conductivity in the same order than human cells, confirms that the measurement capabilities of our device are suitable for electrical cells characterization.