AG Carinae is a massive, evolved supergiant which is thought to be in transition from an O star to a Wolf-Rayet (WR) star and is currently identified as a luminous blue variable (LBV) with logL/solar=6.0. We present an abundance study of the ejecta nebula surrounding AG Car with the aim of elucidating the evolutionary history of the central star. Physical parameters and abundances are derived for five regions across the nebula from high spatial resolution spectroscopy obtained at the Anglo-Australian Telescope (AAT). We derive an average T_e of 6350+/-400K, an n_e of 820+/-170cm^-3, and find that nitrogen (N) is enhanced by a factor of 4.5+/-1.3 and that oxygen (O) is deficient by a factor of 15.1+/-7.2. The derived abundances are compared with those determined for ejecta-type nebulae around WR stars and those predicted by hydrodynamical calculations and stellar evolutionary models. We find that the AG Car nebula is composed of mildly processed material that has not reached the CNO-equilibrium abundances predicted for LBV nebulae. The similarity of the AG Car nebular N abundance to WR nebulae leads us to suggest that the nebulae were ejected at the same evolutionary point, and have undergone no further chemical modification. For AG Car, this point appears to have occurred before the LBV phase because of the observed low N enrichment. Comparison of the observed N abundance with evolutionary model predictions indicates that the AG Car nebula may represent the hydrogen-rich (H- rich) envelope of a red supergiant (RSG). The problem of an RSG progenitor for AG Car is discussed and it is found that the LBV model of Stothers & Chin, incorporating a brief unstable RSG phase, is capable of explaining the observations. We conclude that despite its high luminosity, AG Car has probably experienced a brief RSG phase where it ejected its outer layers to form the currently observed nebula.