Charge transfer (CT) at avoided crossings of excited ionized states of argon dimers is observed using a two-color pump-probe experiment at the free-electron laser in Hamburg (FLASH). The process is initiated by the absorption of three 27-eV-photons from the pump pulse, which leads to the population of Ar^2+*-Ar states. Due to nonadiabatic coupling between these one-site doubly ionized states and two-site doubly ionized states of the type Ar^+*-Ar⁺, CT can take place leading to the population of the latter states. The onset of this process is probed by a delayed infrared (800 nm) laser pulse. The latter ionizes the dimers populating repulsive Ar²⁺ -Ar⁺ states, which then undergo a Coulomb explosion. From the delay-dependent yields of the obtained Ar²⁺ and Ar⁺ ions, the lifetime of the charge-transfer process is extracted. The obtained experimental value of (531 ± 136) fs agrees well with the theoretical value computed from Landau-Zener probabilities.