High-intensity lasers are critical for the exploration of strong field quantum electrodynamics. We report here a demonstration of laser intensity exceeding 10(23) W/cm(2) with the CoReLS petawatt (PW) laser. After wavefront correction and tight focusing with a two-stage adaptive optical system and an f/1.1 (f = 300 mm) off-axis parabolic mirror, we obtained near diffraction-limited focusing with a spot size of 1.1 mu m (FWHM). From the measurement of 80 consecutive laser shots at 0.1 Hz, we achieved a peak intensity of (1.1 +/- 0.2) 10(23) W/cm(2), verifying the applicability of the ultrahigh intensity PW laser for ultrahigh intensity laser-matter interactions. From the statistical analysis of the PW laser shots, we identified that the intensity fluctuation originated from air turbulence in the laser beam path and beam pointing. Our achievement could accelerate the study of strong field quantum electrodynamics by enabling exploration of nonlinear Compton scattering and Breit-Wheeler pair production. (C) 2021 Optical Society of America under the terms the OSA Open Access Publishing Agreement