The competition between proximate electronic phases produces a complex phenomenology in strongly correlated systems. In particular, fluctuations associated with periodic charge or spin modulations, known as density waves, may lead to exotic superconductivity in several correlated materials. However, density waves have been difficult to isolate in the presence of chemical disorder, and the suspected causal link between competing density wave orders and high-temperature superconductivity is not understood. Here we used scanning tunneling microscopy to image a previously unknown unidirectional (stripe) charge-density wave (CDW) smoothly interfacing with the familiar tridirectional (triangular) CDW on the surface of the stoichiometric superconductor NbSe(2). Our low-temperature measurements rule out thermal fluctuations and point to local strain as the tuning parameter for this quantum phase transition. We use this quantum interface to resolve two longstanding debates about the anomalous spectroscopic gap and the role of Fermi surface nesting in the CDW phase of NbSe(2). Our results highlight the importance of local strain in governing phase transitions and competing phenomena, and suggest a promising direction of inquiry for resolving similarly longstanding debates in cuprate superconductors and other strongly correlated materials.