Sr₂RuO₄ is an unconventional superconductor that has attracted widespread study because of its high purity and the possibility that its superconducting order parameter has odd parity. We study the dependence of its superconductivity on anisotropic strain. Applying uniaxial pressures of up to ~1 gigapascals along a 〈100〉 direction (a axis) of the crystal lattice results in the transition temperature (T_c) increasing from 1.5 kelvin in the unstrained material to 3.4 kelvin at compression by ≈0.6%, and then falling steeply. Calculations give evidence that the observed maximum T_c occurs at or near a Lifshitz transition when the Fermi level passes through a Van Hove singularity, and open the possibility that the highly strained, T_c = 3.4 K Sr₂RuO₄ has an even-parity, rather than an odd-parity, order parameter.