  The quasi-2D metal Sr$_2$RuO$_4$ is one of the best characterized
unconventional superconductors, yet the nature of its superconducting order
parameter is still highly debated. This information is crucial to determine the
pairing mechanism of Cooper pairs. Here we use ultrasound velocity to probe the
superconducting state of Sr$_2$RuO$_4$. This thermodynamic probe is
symmetry-sensitive and can help to identify the superconducting order symmetry.
Indeed, we observe a sharp jump in the shear elastic constant $c_{66}$ as the
temperature is raised across the superconducting transition at $T_c$. This
directly implies that the superconducting order parameter is of a two-component
nature. Based on symmetry argument and given the other known properties of
Sr$_2$RuO$_4$, we discuss what states are compatible with this requirement and
propose that the two-component order parameter, namely $\lbrace d_{xz}; d_{yz}
\rbrace$, is the most likely candidate.
