We investigate the formation of weak chimera states in modular networks of electrochemical oscillations during the electrodissulution of nickel in sulfuric acid. In experiment and simulation, we consider two globally coupled populations of highly non-linear oscillators which are weakly coupled through a collective resistance. Without cross coupling, the system exhibits bistability between a one- and a two-cluster state, whose frequencies are distinct. For weak cross coupling and initial conditions for the one- and two-cluster states for populations 1 and 2, respectively, weak chimera dynamics are generated. The weak chimera state exhibits localized frequency synchrony: The oscillators in each population are frequency-synchronized while the two populations are not. The chimera state is very robust: The behavior is maintained for hundreds of cycles for the rather heterogeneous natural frequencies of the oscillators. The experimental results are confirmed with numerical simulations of a kinetic model for the chemical process. The features of the chimera states are compared to other previously observed chimeras with oscillators close to Hopf bifurcation, coupled with parallel resistances and capacitances or with a non-linear delayed feedback. The experimentally observed synchronization patterns could provide a mechanism for generation of chimeras in biological systems, where robust response is essential.