In a four-page published paper with very limited details and explanations, Chao (Biometrika, 1982) presents an elegant and simple to execute algorithm for the selection of a sample of n units that constitute a probability proportional to size sample without replacement from a finite population of N units -- a topic of considerable interest for a long time by those who study probability sampling (see e.g., Madow, 1949; Brewer and Hanif, 1983; Lohr, 2022). According to Chao, his “procedure is sequential in nature… An essential feature of our procedure is that we keep the sample size fixed at n, whereas the population size increases from n to N. Whenever the population 'grows' by one unit, we decide whether this new unit should be sampled. If so, one unit from the old sample is replaced at random by this new unit, thus maintaining the fixed sample size n...”. In this report, we aim to provide some details, clarity, and proofs associated with Chao's elegant method to promote greater consideration of it. One possible consideration might have been the Census Bureau's new Annual Integrated Economic Survey which considered a probability proportional to size sampling plan. Our focus is only on the four-page Chao (1982) paper and awareness of its existence among practicing survey sampling statisticians; no comprehensive literature review of it is attempted.