Consider the problem of a Multiple-Access Channel with a large number of users. In practical scenarios, only a small subset of the users can utilize the channel simultaneously. Thus, user selection is essential. However, since solutions which collect Channel State Information (CSI) from all users and decide on the best subset do not scale when the number of users is large, distributed algorithms for user selection are advantageous. We suggest a distributed user selection algorithm, which selects a group of users to transmit without coordination between all users and without all users sending CSI to the base station. This threshold-based algorithm is analyzed, and its expected capacity in the limit of large number of users is investigated.