Mapping of depth anomalies in the central Pacific reveals a broad, shallow region herein termed the Marquesas--Line Swell. It has the morphology and geoid signature typical of a midplate hotspot swell and probably marks the Tertiary trace of the Marquesas hotspot. The swell is elongate in the NW--SE direction, about 800 m high, and about 1500 km wide. It appears to extend continuously between the Marquesas Islands and the Line Cross Trend. A positive geoid height anomaly over the swell can be separated from the large regional trend. The transfer function between depth anomaly and geoid height is not well defined but is consistent with local isostatic compensation with an average root depth about 30 km (¿40 km, 95% confidence interval) below the swell's surface. Direct spatial comparisons between geoid height and depth anomaly suggest that this root depth is constant along the length of the swell and has a value of about 40 km (¿10 km, 95% confidence interval). The crest of the swell appears to subside as normal seafloor which is only 25 m.y. old, the prediction of the lithospheric thinning hypothesis. A permanent density decrease within the lithosphere can also explain the subsidence and geoid height anomaly; roll-cell dynamic up-lift can explain the subsidence but is difficult to reconcile with the geoid data.