An experiment has been performed with the LULI Multi-TeraWatt Laser. The ac
celeration of electrons injected in a plasma wave generated by the laser wa
kefield mechanism has been observed with a maximum energy gain of 1.5 MeV.
It has been shown that the electrons deflected during the interaction, coul
d scatter on the walls of the experimental chamber, and fake a high-energy
signal. A special effort has been given in the electron detection to separa
te the accelerated electrons signal from the background noise. The experime
ntal results agree with theoretical predictions and numerical simulations w
hen 3D effects on the electron beam are taken into account.