We report traveling-wave quadrature squeezing at 1064 nm in a quasi-phase-matched LiNbO(3) waveguide, avoiding the gain-induced diffraction encountered in bulk squeezing experiments. The 10-mm-long singlemode waveguide parametric amplifier exhibited a gain of 1.9, averaged over the 20-ps mode-locked pulses, with only 0.5 W of peak pump power at 532 nm. Independent waveguides were employed for t...