For experiments in plasma, nuclear, and high-energy physics, there is a strong demand for laser pulses exhibiting relativistic intensity, few-cycle pulse duration, and a very high contrast. Here we present a picosecond-pumped optical parametric chirped pulse amplification (OPCPA) system delivering pulses at 10 Hz repetition rate with the following key parameters: a compressed pulse duration of less than 7 fs (close to the Fourier limit), a contrast of better than 10 11 starting from 1 ps before the main pulse, and a peak intensity of 6.9 × 10 19 W∕cm 2 achieved with an off-axis parabolic mirror (f/1.6). In a proof-of-principle experiment, these pulses were used to generate high harmonics from solid surfaces with photon energies exceeding 55 eV. These results underline the promising perspectives of the reported system for relativistic light-matter interaction experiments and attosecond science.