We present angle-resolved photoemission data from Cu(111). Using a focused 6 eV continuous-wave laser for photoexcitation, we achieve a high effective momentum resolution, enabling detection of the Rashba spin splitting in the Shockley surface state on Cu(111). The magnitude of the spin splitting of Δk∼0.006 Å−1 is surprisingly large and exceeds values predicted for the analogous surface state on Ag(111), but is reproduced by first-principles calculations. We further resolve a kink in the dispersion, which we attribute to electron-phonon coupling.