We have studied the behavior of a liquid crystalline elastomer undergoing a polydomain-monodomain transition. The textures emerging under increasing extensional load have been examined with a combination of optical microscopy, X-ray, and small-angle polarized light scattering. The experimental data are interpreted in terms of reorientation of the local director with increasing extension. The results of this combination of techniques at low extensions are consistent with a two-dimensionally periodic director texture. The amplitude of this modulation decreases continuously as the mesogens are pulled into the extensional direction at high loads. In this manner the samples which are polydomain under no load become essentially monodomain with increasing extension.