  The quantum vacuum shows an intensity-dependent nonlinear index of
refraction. Consequently, we may consider vacuum as a non-linear medium
enabling, at sufficiently high field strengths, a direct interaction of light
with light. In this context, we advocate an experiment to measure
light-by-light scattering by the means of self-focussing of an x-ray beam in
vacuum. Although hard to measure, we argue that for laser beams consisting of
highly energetic photons the beams' power distribution carries a distinctive
enough signature of self-focussing such that an observation at modern
free-electron laser facilities appears possible. Self-focussing also imposes a
limit on the most powerful x-ray beams that may propagate in vacuum being on
the order of $10$ PW for $10$ keV x-rays.
