Using the Fourier Transform Spectrometer at the Canada-France-Hawaii telescope, we obtained high-resolution, high signal-to-noise ratio spectra of seven classical Cepheids at 1.08 mum. We report the first certain detection of the He I lambda10830 line in Cepheids. Three of the Cepheids, X Sgr, eta Aq1, and zeta Gem, were observed with full phase coverage. The He I lambda10830 absorption is present throughout the Cepheid pulsation cycle, which indicates persistent chromospheric heating. This heating is in addition to transient hydrodynamic heating due to pulsationally induced shocks. We find that the He I lambda10830 absorption is systematically blueshifted in at least four Cepheids, indicating a steady outflow in the upper atmosphere. Its velocity variation lags behind the photospheric lines and the cores of Ca II K and Halpha. The time-averaged strength of the He I lambda10830 line in Cepheids, which appears to depend on the T(eff) of the star, is comparable to the average strength of this absorption line in nonvariable yellow supergiants.