Nanoscale waveguides are basic building blocks of integrated optical devices. Especially, waveguides made from nonlinear optical materials, such as lithium niobate, allow access to a broad range of applications using second-order nonlinear frequency conversion processes. Based on a lithium niobate on insulator substrate, millimeter-long nanoscale waveguides were fabricated with widths as small as 200 nm. The fabrication was done by means of potassium hydroxide-assisted ion-beam-enhanced etching. The waveguides were optically characterized in the near infrared wavelength range showing phase-matched second-harmonic generation.