  We report a direct observation of a sharp Kohn-like anomaly in the doubly
degenerate copper-oxygen bond-stretching phonon mode occurring at
$\mathbf{q}\mathrm{=(0.3, 0,0)}$ in La$_{2-x}$Ba$_x$CuO$_{4+\delta}$ with
$\mathrm{x=0.14\pm0.01}$, thanks to the high $\mathbf{Q}$ resolution of
inelastic x-ray scattering. This anomaly is clearly seen when the inelastic
signal is analysed using a single mode but is also consistent with a two mode
hypothesis possibly due to a splitting of the degenerate modes due to symmetry
breaking stripes. Our observation shows that the effect persists at the stripe
propagation vector in a superconducting system close to optimal doping.
