  Despite significant achievements in characterizing the properties of
Sr$_2$RuO$_4$ over the last three decades, the precise nature of its electronic
ground state is still unresolved. In this work, we provide a missing piece of
the puzzle by uncovering evidence of electronic nematic order in the normal
state of Sr$_2$RuO$_4$, revealed by ultrafast time-resolved optical dichroism
measurements of uniaxially strained thin films. This nematic order, whose
domains are aligned by the strain, spontaneously breaks the four-fold
rotational symmetry of the crystal. The temperature dependence of the dichroism
resembles an Ising-like order parameter, and optical pumping induces a coherent
oscillation of its amplitude mode. A microscopic model of intra-unit-cell
nematic order is presented, highlighting the importance of Coulomb repulsion
between neighboring oxygen $p$-orbitals. The existence of electronic nematic
order in the normal state of Sr$_2$RuO$_4$ may have consequences for the form
and mechanism of superconductivity in this material.
