We present a sensitive radio image of the nebula associated with the luminous blue variable star HR Carinae. This nebula is small and difficult to observe optically because of the presence of the bright star. The radio image shows the filaments in the outer regions of the nebula as seen in optical coronagraphic images. The core of the nebula is elongated north-south on the sky. A compact source associated with HR Car is clearly detected at the western edge of the nebula, but the nebula is very asymmetric with respect to the star, lying almost entirely to the east. The inner nebula shows no evidence for the bipolar structure inferred to exist from observations of the outer nebula: the symmetry axes in the inner nebula are 45° away from the bipolar axes. If the compact radio emission at the location of the star is a classical stellar wind source, we estimate a mass-loss rate for ionized gas of 1.8x10–5 M☉.yr–1. The mass in the central core of the nebula is about 0.3 M☉, while the outer nebula may contain as much as 0.5 M☉. We believe that a colliding winds explanation of the nebula is unlikely; a symbiotic-like explanation in which ionization of neutral ejecta is provided by a hot companion star may be possible if the companion star is on the far side of the nebula and heavily extincted, but it is not clear whether the properties required of this star are compatible with the fact that it is not detected in a 10 µm image. A B0 V companion without much dust may be consistent with the data.