The 700-km-long Chaman fault (CF) marks the western edge of the plate boundary between India and Eurasia. Although global plate models predict 2.3-3.6 cm/yr left-lateral motion between both plates, the fault is known to have hosted few earthquakes in historical times. Recent geodetic measurements attested the presence of aseismic slip locally. To detail the interplay between fast and slow slip along the CF, we build three Interferometric Synthetic-Aperture Radar time series of ground deformation covering the whole fault length over 5 years (2014-2019). We find that most of the active fault trace slips aseismically and continuously. From south to north, we identify three creeping fault portions: the Nushki, Central, and Qalat segments of lengths between 80 and 130 km. The loading rate is 1.2 +/- 0.3 cm/yr for the two southernmost portions, while it is about 0.7 +/- 0.2 cm/yr for the Qalat segment. The Central segment and the nearby locked segments have hosted the largest known historical earthquakes on the CF, and three moderate magnitude earthquakes in our observation period. We image these earthquakes for which modeled slip at depth (M-w 5-5.6), time series of surface slip and deformation patterns argue toward large triggered aseismic slip. The June 2018 event displays postseismic moment 3-15 times greater than coseismic moment. Over the two decades covered by geodetic observations, continuous or triggered aseismic slip dominates along most of the fault and co-locates with earthquakes. We observe that fault geometrical complexities delimit active segments and may be responsible for the kilometer-scale intertwining between seismic and aseismic events. Plain Language Summary The Chaman fault (CF) separates Indian and Eurasian tectonic plates moving at about 3 cm/yr with respect to each other. This fault is known to have hosted very few earthquakes (sudden and rapid slip) in historical times, and appears to slip slowly. We measure slip on the CF with radar satellite images covering 2014-2019, and assess the average amount of slip attributed to earthquakes over the past century. We identify three 80-130-km-long portions of the 700-km-long fault that slip silently, without radiating seismic waves, at rates reaching 1.2 +/- 0.3 cm/year along the southern half, and 0.7 +/- 0.2 cm/year in the north. The largest historical earthquakes and three earthquakes of moderate size in our observation period occurred on the central part of the CF. We image the surface deformation induced by these three earthquakes and find that they were followed by significant slow slip on the fault, especially the third event in June 2018. Since the 2000s space-based measurements indicate that the slow mode of slip dominates on the CF plane and co-locates with earthquakes. Changes of fault orientation may delimit portions of the fault which either slip slowly or break into fast earthquakes.