We report on the generation of continuous-wave (cw) ultraviolet (UV) laser light at λ=278 nm by optical frequency doubling of visible light in β-BaB₂O₄ waveguides. Ridge-type waveguides were produced by He⁺ implantation, photolithography masking, and plasma etching. The final waveguides have core dimension of a few μm² and show transmission losses of 5 dB/cm at 532 nm and less than 10 dB/cm at 266 nm. In our first experiments, a second harmonic power of 24 μW has been generated at 278 nm in an 8 mm long waveguide pumped by 153 mW at 556 nm.