When electrons in a solid are excited by light, they can alter the free energy landscape and access phases of matter that are out of reach in thermal equilibrium. This accessibility becomes important in the presence of phase competition, when one state of matter is preferred over another by only a small energy scale that, in principle, is surmountable by the excitation. Here, we study a layered compound, LaTe3, where a small lattice anisotropy in the a–cplane results in a unidirectional charge density wave (CDW) along the caxis1,2. Using ultrafast electron diffraction, we find that, after photoexcitation, the CDW along the caxis is weakened and a different competing CDW along the aaxis subsequently emerges. The timescales characterizing the relaxation of this new CDW and the reestablishment of the original CDW are nearly identical, which points towards a strong competition between the two orders. The new density wave represents a transient non-equilibrium phase of matter with no equilibrium counterpart, and this study thus provides a framework for discovering similar states of matter that are ‘trapped’ under equilibrium conditions.