The D-alpha emission time-series from the TCV tokamak was investigated fora large set of ELMy discharges, to determine whether fluctuations in the time delay between ELMs are the result of noise only, or whether a deterministic process in a chaotic state exists, as suggested by results on JT-60U (Bak et al 1999 Phys. Rev. Lett. 83 1339). This study was carried out by searching the time-series of each discharge for transient sequences that are generic to chaotic systems, called unstable periodic orbits (UPOs). By taking a statistical approach, a subset of discharges with q(95) greater than 2.6 were shown to contain many more UPOs than could be expected if the dynamical system was noise dominated, and the properties of these UPOs were found to exhibit systematic variations with plasma parameters. Specifically, the period of the unstable fixed point DeltaT* was found to scale independently with the plasma current, density and the inner plasma-wall distance. In a number of cases, two separate fixed points were found to co-exist during the same discharge.