The concept of a large intelligent surface (LIS) has recently emerged as a promising wireless communication paradigm that can exploit the entire surface of man-made structures for transmitting and receiving information. An LIS is expected to go beyond massive multiple-input multiple-output (MIMO) system, insofar as the desired channel can be modeled as a perfect line-of-sight. To understand the fundamental performance benefits, it is imperative to analyze its achievable data rate, under practical LIS environments and limitations. In this paper, an asymptotic analysis of the uplink data rate in an LIS-based large antenna-array system is presented. In particular, the asymptotic LIS rate is derived in a practical wireless environment where the estimated channel on LIS is subject to estimation errors and interference channels are spatially correlated Rician fading channels. Moreover, the occurrence of the channel hardening effect is analyzed and the performance bound is asymptotically derived for the considered LIS system. The analytical asymptotic results are then shown to be in close agreement with the exact mutual information as the numbers of antennas and devices increases without bounds. Moreover, the derived ergodic rates show that noise and interference from estimation errors and the non-line-of-sight path become negligible as the number of antennas increases. Simulation results show that an LIS can achieve a performance that is comparable to conventional massive MIMO with improved reliability and a significantly reduced area for antenna deployment.