Context. The Kelvin-HeImholtz (KH) instability is a nonlinear shear-driven instability that develops at the interface between shear flows in plasmas. KH waves have been inferred in various astrophysical plasmas, and have been observed in situ at the magnetospheric boundaries of solar-system planets and through remote sensing at the boundaries of coronal mass ejections. Aims. KH waves are also expected to develop at flow shear interfaces in the solar wind. While they were hypothesized to play an important role in the mixing of plasmas and in triggering solar wind fluctuations, their direct and unambiguous observation in the solar wind was still lacking. Methods. We report in situ observations of quasi-periodic magnetic and velocity field variations plausibly associated with KH waves using Solar Orbiter during its cruise phase. They are found in a shear layer in the slow solar wind in the close vicinity of the heliospheric current sheet. An analysis was performed to derive the local configuration of the waves. A 2D magnetohydrodynamics simulation was also set up with approximate empirical values to test the stability of the shear layer. In addition, magnetic spectra of the event were analyzed. Results. We find that the observed conditions satisfy the KH instability onset criterion from the linear theory analysis, and its development is further confirmed by the simulation. The current sheet geometry analyses are found to be consistent with KH wave development, albeit with some limitations likely owing to the complex 3D nature of the event and solar wind propagation. Additionally, we report observations of an ion jet consistent with magnetic reconnection at a compressed current sheet within the KH wave interval. The KH activity is found to excite magnetic and velocity fluctuations with power law scalings that approximately follow k-5/3 and k-2.8 in the inertial and dissipation ranges, respectively. Finally, we discuss reasons for the lack of in situ KH wave detection in past data. Conclusions. These observations provide robust evidence of KH wave development in the solar wind. This sheds new light on the process of shear-driven turbulence as mediated by the KH waves with implications for the driving of solar wind fluctuations.