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A new global network for high-resolution H-alpha full-disk observations of the sun has been established at the Big Bear Solar Observatory (U.S.A.), the Kanzelhohe Solar Observatory (Austria), and the Yunnan Astronomical Observatory (China). Each of the three stations have a 2K x 2K pixel CCD detector available to monitor the sun with a spatial resolution of 1 arcsec per pixel and a cadence of at least 1 image per minute. Having high-cadence data from three observing stations available enables us to accurately track solar rotation rates and meridional motions by local correlation (LCT) and feature tracking techniques. This includes, e.g., tracking over several days the motions around active regions. After an overview of the new H-alpha: network and its scientific objectives, we present and discuss the first preliminary results of the determination of the chromospheric differential rotation by LCT from a high-cadencence time-series of H-alpha full-disk images. The obtained equatorial rotation rate of 13.3044 deg/day (2.6876 mu rad/s) agrees well with the values obtained by other authors. Finally, we briefly outline our future plans for the continuation of this work.