Optical waveguides made from periodically poled materials provide high confinement of light and enable the generation of new wavelengths via quasi-phase-matching, making them a key platform for nonlinear optics and photonics. However, such devices are not typically employed for high-harmonic generation. Here, using 200-fs, 10-nJ-level pulses of 4100 nm light at 1 MHz, we generate high harmonics up to the 13th harmonic (315 nm) in a chirped, periodically poled lithium niobate (PPLN) waveguide. Total conversion efficiencies into the visible--ultraviolet region are as high as 10 percent. We find that the output spectrum depends on the waveguide poling period, indicating that quasi-phase-matching plays a significant role. In the future, such periodically poled waveguides may enable compact sources of ultrashort pulses at high repetition rates and provide new methods of probing the electronic structure of solid-state materials.