The Dzyaloshinskii-Moriya Interaction (DMI) has recently attracted considerable interest owing to its fundamental role in the stabilization of chiral spin textures in ultrathin ferromagnets, which are interesting candidates for future spintronic technologies. Here we employ a scanning nano-magnetometer based on a single nitrogen-vacancy (NV) defect in diamond to locally probe the strength of the interfacial DMI in CoFeB/MgO ultrathin films grown on different heavy metal underlayers X=Ta,TaN, and W. By measuring the stray field emanating from DWs in micron-long wires of such materials, we observe deviations from the Bloch profile for TaN and W underlayers that are consistent with a positive DMI value favoring right-handed chiral spin structures. Moreover, our measurements suggest that the DMI constant might vary locally within a single sample, illustrating the importance of local probes for the study of magnetic order at the nanoscale.