Space-borne Differential Interferometric Synthetic Aperture Radar (DInSAR) has been extensively used in the last two decades to measure ground surface deformation, providing key information for the characterization and understanding of many natural and anthropogenic processes. However, conventional DInSAR technique measures only one component of the surface deformation (i.e. the satellite's line-of-sight (LOS)), causing the interpretation of DInSAR measurements to be challenging and potentially narrowing the understanding of the mechanisms and dynamics of the deformation processes at work. Presently available methods that estimate 3D surface deformation from DInSAR generally operate on individual interferograms and therefore do not produce 3D surface deformation time series. However, the availability of time series is essential for studying surface deformation processes, bringing information on, e.g., temporally and spatially-variable external forcing conditions and characteristics of future deformation patterns. The Multidimensional Small Baseline Subset (MSBAS) method was already able to produce 2D (east and vertical) surface deformation time series from multi-tracks and multi-sensors DInSAR data. Here we propose a novel version of the MSBAS (MSBAS-3D) method that can produce 3D (north, east, and vertical) surface deformation time series from ascending and descending DInSAR data. This new method proposes measuring the surface deformation for processes producing motion parallel to the surface, such as landslides and glacier flows, while conserving the DInSAR accuracy. The ability of MSBAS-3D to capture the full 3D deformation pattern of processes with a surface signature is illustrated for a large, slow-moving, deep-seated landslide, for which long DInSAR and dGNSS time series, as well as ground truth data, are available. Surface deformation is measured over a four-year period using 1D (LOS), 2D and 3D MSBAS methods, and the advantages and limitations of each approach are described. In this case, the novel MSBAS-3D technique produces superior results that greatly simplify interpretation of the processes at work. The MSBAS-3D software can be downloaded from http://insar.ca/.