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Consider a Markov chain on Z+ with reflecting barrier at 0 such that jumps of the chain outside of 0 are iid with mean zero and finite variance. It is assumed that the jump from 0 has a distribution that belongs to the domain of attraction of non-negative stable law. It is proved that under natural scaling of a space and a time a limit of this scaled Markov chain is a Brownian motion with some Wentzell’s boundary condition at 0.