This paper demonstrates for the first time that centimeter-accurate positioning is possible based on data sampled from a smartphone-quality Global Navigation Satellite System (GNSS) antenna. Centimeter-accurate smart-phone positioning will enable a host of new applications such as globally-registered fiduciary-marker-free augmented reality and location-based contextual advertising, both of which have been hampered by the several-meter-level errors in traditional GNSS positioning. An empirical analysis of data collected from a smartphone-grade GNSS antenna reveals the antenna to be the primary impediment to fast and reliable resolution of the integer ambiguities which arise when solving for a centimeter-accurate carrier-phase differential position. The antenna's poor multipath suppression and irregular gain pattern result in large time-correlated phase errors which significantly increase the time to integer ambiguity resolution as compared to even a low-quality stand-alone patch antenna. The time to integer resolution and to a centimeter-accurate fix - is significantly reduced when more GNSS signals are tracked or when the smartphone experiences gentle wavelength-scale random motion.