A radar scatterometer operates by transmitting a pulse of microwave energy toward the ocean's surface and measuring the normalized (per-unit-surface) radar backscatter coefficient (σ°). The primary application of scatterometry is the measurement of near-surface ocean winds. By combining σ° measurements from different azimuth angles, the 10 m vector wind can be determined through a Geophysical Model Function (GMF), which relates wind and backscatter. This paper proposes a mission concept for the measurement of both oceanic winds and surface currents, which makes full use of earlier C-band radar remote sensing experience. For the determination of ocean currents, in particular, the novel idea of using two chirps of opposite slope is introduced. The fundamental processing steps required to retrieve surface currents are given together with their associated accuracies. A detailed description of the mission proposal and comparisons between real and retrieved surface currents are presented. The proposed ocean Doppler scatterometer can be used to generate global surface ocean current maps with accuracies better than 0.2 m/s at a spatial resolution better than 25 km (i.e., 12.5 km spatial sampling) on a daily basis. These maps will allow gaining some insights on the upper ocean mesoscale dynamics. The work lies at a frontier, given that the present inability to measure ocean currents from space in a consistent and synoptic manner represents one of the greatest weaknesses in ocean remote sensing.