We consider a single-hop wireless network consisting of alpha . N sources, where alpha >= 1 is a scaling factor. These sources are randomly distributed around a single base-station/access-point and utilize the IEEE 802.11 standard for medium access control. The transmission speed of each node C, the minimum contention window CWmin, and the maximum contention window CWmax, are all multiplied by the scaling factor alpha. Further, all protocol time-intervals are multiplied by 1/alpha. We show that as the scaling factor alpha increases, the packet delays become independent of alpha, and therefore, of the number of sources (alpha . N) sharing the wireless channel. At the same time, the user's perceived throughput and drop ratio remain almost invariant. This result is not only of theoretical interest, but also of great practical interest, as it clearly identifies the set of the system's parameters that we should aim to (simultaneously) scale in future versions of the IEEE 802.11 protocol (or in new protocols that utilize similar ideas), so that the system can support a very large number of users, while continuing to deliver to each user at least as good performance as before.