Abstract: We report on a search for the flavor-changing neutral-current decay D-0 -> mu(+)mu(-) in p (p) over bar collisions at root s = 1.96 TeV using 360 pb(-1) of integrated luminosity collected by the CDF II detector at the Fermilab Tevatron collider. A displaced vertex trigger selects long-lived D-0 candidates in the mu(+)mu(-), pi(+)pi(-), and K-pi(+) decay modes. We use the Cabibbo-favored D-0 -> K-pi(+) channel to optimize the selection criteria in an unbiased manner, and the kinematically similar D-0 -> pi(+)pi(-) channel for normalization. We set an upper limit on the branching fraction B(D-0 -> mu(+)mu(-)) < 2.1 X 10(-7) (3.0 X 10(-7)) at the 90% (95%) confidence level.