The Dα emission time-series from the TCV tokamak wasinvestigated for a large set of ELMy discharges, to determine whetherfluctuations in the time delay between ELMs are the result of noiseonly, or whether a deterministic process in a chaotic state exists, assuggested by results on JT-60U (Bak \textit{et al} 1999 \textit{Phys. Rev. Lett.} \textbf{83} 1339). This study was carried out by searchingthe time-series of each discharge for transient sequences that aregeneric to chaotic systems, called unstable periodic orbits (UPOs). Bytaking a statistical approach, a subset of discharges with q95greater than 2.6 were shown to contain many more UPOs than could beexpected if the dynamical system was noise dominated, and the propertiesof these UPOs were found to exhibit systematic variations with plasmaparameters. Specifically, the period of the unstable fixed point ΔT* was found to scale independently with the plasma current,density and the inner plasma-wall distance. In a number of cases, twoseparate fixed points were found to co-exist during the same discharge.