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We investigate the LHC and Higgs Factory prospects for measuring the CP phasein the Higgs-tau-tau coupling. Currently this phase can be anywhere between 0degrees (CP even) and 90 degrees (CP odd). A new, ideal observable isidentified from an analytic calculation for the $\tau^\pm \to \rho^\pm\nu \to\pi^\pm \pi^0 \nu$ channel. It is demonstrated to have promising sensitivity atthe LHC and superior sensitivity at the ILC compared to previous proposals. Ourobservable requires the reconstruction of the internal substructure of decayingtaus but does not rely on measuring the impact parameter of tau decays. It isthe first proposal for such a measurement at the LHC. For the 14 TeV LHC, weestimate that about 1 ab$^{-1}$ data can discriminate CP-even versus CP-odd atthe $5\sigma$ level. With 3 ab$^{-1}$, the CP phase should be measurable to anaccuracy of $\sim 11$ degrees. At an $e^+e^-$ Higgs Factory, we project that a250 GeV run with 1 ab$^{-1}$ luminosity can measure the phase to $\sim 4.4$degrees accuracy.

Measuring CP Violation in $h \to \tau^+ \tau^-$ at Colliders