We study the eccentricity distribution of a thick-disc sample of stars (defined as those with Vy > 50 km s−1 and 1 < |z|/kpc < 3) observed in the Radial Velocity Experiment (RAVE). We compare this distribution with those obtained in four simulations of galaxy formation taken from the literature as compiled by Sales et al. Each simulation emphasizes different scenarios for the origin of such stars (satellite accretion, heating of a pre-existing thin disc during a merger, radial migration, and gas-rich mergers). We find that the observed distribution peaks at low eccentricities and falls off smoothly and rather steeply to high eccentricities. This finding is fairly robust to changes in distances and to plausible assumptions about thin-disc contamination. Our results favour models where the majority of stars formed in the Galaxy itself on orbits of modest eccentricity and disfavour the pure satellite accretion case. A gas-rich merger origin where most of the stars form ‘in situ’ appears to be the most consistent with our data.