Poisson approximation in ${\chi }^2$ distance by Chen-Stein approach

The main purpose of the paper is to investigate the possibility of applying Chen-Stein approach to estimate the ${\chi }^2$ distance between Poisson distribution and a sum of independent indicators. Earlier results concerning ${\chi }^2$ distance between above mentioned distributions either used analytical approach heavily based on the analysis of the generating functions or on rather lengthy and complicated elementary calculations. Applying Chen-Stein approach we succeed in providing a very quick proof of upper bounds for ${\chi }^2$ distance that are of comparable strength to the earlier estimates obtained by other approaches.