On June 19, 2020 at 20:05:07 UTC, a fireball lasting 5.5 s was observed above Western Australia by three Desert Fireball Network observatories. The meteoroid entered the atmosphere with a speed of 14.00±0.17 km s-1 and followed a 58° slope trajectory from a height of 75 km down to 18.6 km. Despite the poor angle of triangulated planes between observatories (29°) and the large distance from the observatories, a well-constrained kilo-size main mass was predicted to have fallen just south of Madura in Western Australia. However, the search area was predicted to be large due to the trajectory uncertainties. Fortunately, the rock was rapidly recovered along the access track during a reconnaissance trip. The 1.072 kg meteorite called Madura Cave was classified as an L5 ordinary chondrite. The calculated orbit is of Aten type (mostly contained within the Earth's orbit), only the second time a meteorite was observed on such an orbit, after Bunburra Rockhole. Dynamical modeling shows that Madura Cave has been in near-Earth space for a very long time. The dynamical lifetime in near-Earth space for the progenitor meteoroid is predicted to be ~87 Myr. This peculiar orbit also points to a delivery from the main asteroid belt via the ν6 resonance, and therefore an origin in the inner belt. This result contributes to drawing a picture for the existence of a present-day L chondrite parent body in the inner belt.