k-mutual exclusion is an important problem for resourceintensive peer-to-peer applications ranging from aggregation to file downloads. In order to be practically useful, k-mutual exclusion algorithms not only need to be safe and live, but they also need to be fair across hosts. We propose a new solution to the k-mutual exclusion problem that provides a notion of time-based fairness. Specifically, our algorithm attempts to minimize the spread of access time for the critical resource. While a client's access time is the time between it requesting and accessing the resource, the spread is defined as a system-wide metric that measures some notion of the variance of access times across a homogeneous host population, e.g., difference between max and mean. We analytically prove the correctness of our algorithm, and evaluate its fairness experimentally using simulations. Our evaluation under two settings - a LAN setting and a WAN based on the King latency data set - shows even with 100 hosts accessing one resource, the spread of access time is within 15 seconds.