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Transition-metal dichalcogenides (TMDs) have emerged as a rich platform hosting novel states of quantum matter. One such is the Cooper-pair density wave (PDW) state in which the electron-pair density spatially modulates at one or more wavevectors. Using atomic-resolution scanned Josephson- tunneling microscopy, we visualize the electron-pair density and discover a PDW state in the canonical TMD superconductor NbSe₂. We show that the PDW shares the wavevectors of the preexisting charge density wave (CDW) and is directly coupled to the background superconductivity as evidenced by their mutual decay into a superconducting vortex core. However, simultaneous PDW and CDW imaging reveals them to be spatially distinct at atomic-scale due to a global spatial phase difference |δΦΙ≈2π/3 (one unit cell) between the two states. Given the abundance of TMDs sustaining both CDW and superconductivity, detection and visualization of PDW in NbSe2 presages abundant new PDW physics.