Using high-resolution magnetic field data from the STEREO mission, we have observed strong narrow-band ion cyclotron waves (ICWs) in the solar wind near 1 AU. The waves propagate nearly parallel to the magnetic field and are below the local proton gyrofrequency in the solar wind frame. Because the twin STEREO spacecraft were far away from any planet, including the Earth, the waves do not have a planetary source. The ICWs often appear when the interplanetary magnetic field is more radial than the nominal Parker spiral. Since the wave frequency in the spacecraft frame is higher than the local proton gyrofrequency, the waves are not locally generated by ion pickup. Observations are consistent with wave generation closer to the Sun and outward transport by the super-Alfvénic solar wind. The waves are intrinsically left-hand polarized in the solar wind frame, but appear to be both left- and right-handed in the spacecraft frame, associated with outward and inward propagation, respectively. The relative amplitudes of the left-handed and right-handed waves support the closer-to-Sun generation scenario.