Random telegraph noise (RTN) owns its very name to its assumed stochastic nature. In this paper, we follow up previous works that questioned this stochastic nature, and we investigate this assumption using experimentally measured noise coming from properly biased Ni/HfO2 unipolar Resistive RAM memristor nanodevices. We have used established, well–known tools from nonlinear theory to examine the current–noise temporal series. Evaluation results show that this series appears to exhibit not a stochastic, but a deterministic chaotic behavior, also demostrating interesting fractal characteristics in 2D and 3D phase space projections. The presented results clearly advocate for a strong component of complex (chaotic) fluctuation of deterministic origin, instead of a typical (fully stochastic) RTN. This result could pave the path for an enhanced understanding of the mechanisms behind RTN emergence, as well as improve its noise models. •We have analyzed experimental time series RTN from Ni/HfO2 unipolar Resistive RAM memristor nanodevices.•Established nonlinear dynamics evaluation tools have been utilized in order to characterize•The recorded RTN has been proved to be deterministic chaotic, possessing a fractal structure.•The studied nanodevice dynamics can embedded in a 5-dimensional phase space.