HR8799 is a young (20–160 Myr) A-dwarf main sequence star with a debris disc detected by IRAS (InfraRed Astronomical Satellite). In 2008, it was one of two stars around which exoplanets were directly imaged for the first time. The presence of three Jupiter-mass planets around HR8799 provoked much interest in modelling the dynamical stability of the system. Initial simulations indicated that the observed planetary architecture was unstable on timescales much shorter than the lifetime of the star (~105 yr). Subsequent models suggested that the system could be stable if the planets were locked in a 1:2:4 mutual mean motion resonance (MMR). In this work, we have examined the influence of varying orbital eccentricity and the semi-major axis on the stability of the three-planet system, through dynamical simulations using the MERCURY n-body integrator. We find that, in agreement with previous work on this system, the 1:2:4 MMR is the most stable planetary configuration, and that the system stability is dominated by the interaction between the inner pair of planets. In contrast to previous results, we find that with small eccentricities, the three-planet system can be stable for timescales comparable to the system lifetime and, potentially, much longer.