The emission at the second harmonic (2&ohgr;e) of the plasma frequency from self-consistent Langmuir solitons is calculated. The theory predicts, in a natural way, the observed transition from the region where the intensity is linearly proportional to the electron flux to the region where the radio intensity is proportional to the square of the electron flux. A detailed comparison of the radiation observed at 2&ohgr;e for the burst of 31 March 1976, 18:10 UT with the one expected on the assumption of radiation from solitons, using the correlated in situ measurements of the electric fields at &ohgr;e and their spatial structure provides strong evidence that, for the first time, Langmuir solitons have been observed in space.