When electrons in a solid are excited with light, they can alter the free energy landscape and access phases of matter that are beyond reach in thermal equilibrium. This accessibility becomes of vast importance 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 light. Here, we study a layered compound, LaTe$_3$, where a small in-plane (a-c plane) lattice anisotropy results in a unidirectional charge density wave (CDW) along the c-axis. Using ultrafast electron diffraction, we find that after photoexcitation, the CDW along the c-axis is weakened and subsequently, a different competing CDW along the a-axis 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 unleashing similar states of matter that are trapped under equilibrium conditions.
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