  We search for the semi-inclusive process B_s^0 --> D_s^(*)D_s^(*) using 2.8
fb^-1 of ppbar collisions at s^(1/2) = 1.96 TeV recorded by the D0 detector
operating at the Fermilab Tevatron Collider. We observe 26.6 +/- 8.4 signal
events with a significance above background of 3.2 standard deviations yielding
a branching ratio of Br(B_s^0 --> D_s^(*)D_s^(*)) = 0.035 +/- 0.010(stat) +/-
0.011(syst). Under certain theoretical assumptions, these double-charm final
states saturate CP-even eigenstates in the B_s^0 decays resulting in a width
difference of Delta_Gamma_s^CP/Gamma_s = 0.072 +/- 0.021(stat) +/- 0.022(syst).
