In this paper, a simple system showing chaotic behavior is introduced. It is based on the well-known concept of cellular neural networks (CNNs), which have already given good results in generating complex dynamics. The peculiarity of the CNN model consists in the fact that it replaces the traditional first-order cell with a noninteger-order one. The introduction of the fractional cell, with a suitable choice of the coupling parameters, leads to the onset of chaos in a simple two-cell system. A theoretical approach, based on the harmonic balance theory, has been used to investigate the existence of chaos. A circuit realization of the proposed fractional two-cell chaotic CNN is reported and the corresponding strange attractor is also shown.