The measurement of peak laser intensities exceeding 10^{20} \text{W/cm^2}
is in general a very challenging task. We suggest a simple method to accurately
measure such high intensities up to about 10^{23} \text{W/cm^2}, by
colliding a beam of ultrarelativistic electrons with the laser pulse. The
method exploits the high directionality of the radiation emitted by
ultrarelativistic electrons via nonlinear Thomson scattering. Initial electron
energies well within the reach of laser wake-field accelerators are required,
allowing in principle for an all-optical setup. Accuracies of the order of 10%
are theoretically envisaged.Comment: 4 pages, 2 figure