Implementation of 1-bit Digital-to-analog converters (DACs) at base station (BS) antennas reduces power consumption and hardware complexity for a downlink massive MIMO system while introducing non-linear impairments in the transmitted signal. Through low complexity quantized linear precoding at the BS it is possible to mitigate detrimental effects of these impairments on the received signal. For a small number of users, however, quantization noise components across BS antennas become highly correlated, deteriorating per-user performance severely. In this paper, we improve performance and reduce correlation among quantization noise components by adding colored dither to the signal before DAC. Using the Bussgang decomposition up to the third order harmonics, we estimate the closed form asymptotic expression for per-user signal to quantization, interference and noise ratio (SQINR) of the received signal as a function of the dither power. We evaluate optimum dither power by maximizing SQINR.