Hemodynamic changes occur in stroke and neurodegenerative diseases. Developing imaging techniques allowing the in vivo visualization and quantification of cerebral blood flow would help better understand the underlying mechanism of those cerebrovascular diseases. 3D ultrasound localization microscopy (ULM) is a novel technology that can map the microvasculature of the brain at large depth and has been mainly used until now in rodents. Here, we demonstrated the feasibility of 3D ULM of the nonhuman primate (NHP) brain with a single 256-channels programmable ultrasound scanner. We achieved a highly resolved vascular map of the macaque brain at large depth in presence of craniotomy and durectomy using an 8-MHz multiplexed matrix probe. We were able to distinguish vessels as small as 26.9 {\mu}m. We also demonstrated that transcranial imaging of the macaque brain at similar depth was feasible using a 3-MHz probe and achieved a resolution of 60.4 {\mu}m. This work paves the way to clinical application of 3D ULM.