  We propose and use a technique to measure the transverse emittance of a
laser-wakefield accelerated beam of relativistic electrons. The technique is
based on the simultaneous measurements of the electron beam divergence given by
$v_{\perp}/v_{\parallel}$, the measured longitudinal spectrum
$\gamma_\parallel$ and the transverse electron bunch size in the bubble
$r_{\perp}$. The latter is obtained via the measurement of the source size of
the x-rays emitted by the accelerating electron bunch in the bubble. We measure
a \textit{normalised} RMS beam transverse emittance $<0.5$ $\pi$ mm$\:$mrad as
an upper limit for a spatially gaussian, spectrally quasi-monoenergetic
electron beam with 230 MeV energy in agreement with numerical modeling and
analytic theory in the bubble regime.
