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One-dimensional (1D) topological superconductivity is a state of matter that is not found in nature. However, it can be realised, for example, by inducing superconductivity into the quantum spin Hall edge state of a two-dimensional topological insulator. Because topological superconductors are proposed to host Majorana zero modes, they have been suggested as a platform for topological quantum computing. Yet, conclusive proof of 1D topological superconductivity has remained elusive. Here, we employ low-temperature scanning tunnelling microscopy to show 1D topological superconductivity in a van der Waals heterostructure by directly probing its superconducting properties, instead of relying on the observation of Majorana zero modes at its boundary. We realise this by placing the two-dimensional topological insulator monolayer WTe$_2$ on the superconductor NbSe$_2$. We find that the superconducting topological edge state is robust against magnetic fields, a hallmark of its triplet pairing. Its topological protection is underpinned by a lateral self-proximity effect, which is resilient against disorder in the monolayer edge. By creating this exotic state in a van der Waals heterostructure, we provide an adaptable platform for the future realization of Majorana bound states. Finally, our results more generally demonstrate the power of Abrikosov vortices as effective experimental probes for superconductivity in nanostructures., Comment: 13 pages, 4 figures