The transverse emittance of a relativistic electron beam generated by the interaction of a high-intensity laser with an underdense plasma has been measured with the "pepper-pot" method. For parameters pertaining to the forced laser wakefield regime, we have measured an emittance as low as (2.7+/-0.9) pi mm mrad for (55+/-2) MeV electrons. These measurements are consistent with 3D particle-in-cell simulations of the experiment, which additionally show the existence of a relatively large halo around the beam core.