By using an electron-photon coincidence method the photon emission asymmetry in the elementary process of bremsstrahlung from transversely polarized electrons was measured for fixed directions of the outgoing electrons and coplanar geometry. For an electron beam of 300 keV incident on a gold target, emission asymmetries up to 35% were found. Even in the case of no deflection of the decelerated outgoing electrons a nonzero photon emission asymmetry was observed. The measurements are a proper test for theories going beyond the first Born approximation.PACS numbers: 34.80.-i Bremsstrahlung emitted by an electron scattered in the Coulomb field of an atomic nucleus is a process suitable to study the coupling of radiation with matter. The aim of our experiment is to investigate the role of spin-orbit interaction in this fundamental radiation process. An important observable is the angular asymmetry of bremsstrahlung emitted by a transversely polarized electron beam where the spin direction is perpendicular to the photon emission plane, defined by the momenta of the incoming electron and the emitted photon. Disregarding the decelerated outgoing electrons such left-right photon emission asymmetries have been measured by several groups [1,2] and recently in our laboratory [3] in order to clear up discrepancies with calculations which appeared in previous work [2]. We found good agreement with the theoretical predictions of a partial wave calculation of Tseng and Pratt [4]. However, since in all these experiments only the emitted photons have been observed, the results are necessarily averaged over all electron scattering angles. Therefore the test of theoretical predictions is not as strong as it could be. To get detailed information on the elementary collision process we performed a coincidence measurement between outgoing electrons and photons emitted by a transversely polarized beam. The results of the measurement are presented in this Letter.Using unpolarized electrons such an electron-photon coincidence experiment was first performed in our laboratory in 1966 [5]. Its continuation and the work of other groups were reviewed by Nakel [6]. In all these (coplanar) coincidence measurements it proved that there is a strong angular correlation with the photons being predominantly emitted on the same side relative to the primary beam as the decelerated electrons. This feature can be used to illustrate in a very simple way the photon emission asymmetry from transversely polarized electrons observed in noncoincidence experiments by additionally taking into account the asymmetric scattering of the radiating electrons due to spin-orbit coupling (analogous to Mott scattering). However, to interpret the results of our present electron-photon coincidence experiment revealing the structure of the elementary bremsstrahlung process, the simple picture does not suffice. This becomes particularly clear in the special case where the electron detector is put into the 0° position, i.e., in the direction of the primary beam. Here the outgoi...