In 1979, David Fabian found a complete game of two-person Chinese Checkers in 30 moves (15 by each player). This solution requires that the two players cooperate to generate a win as quickly as possible for one of them. We show, using computational search techniques, that no shorter game is possible. We also consider a solitaire version of Chinese Checkers where one player attempts to move her pieces across the board in as few moves as possible. In 1971, Octave Levenspiel found a solution in 27 moves; we demonstrate that no shorter solution exists. To show optimality, we employ a variant of A* search, as well as bidirectional search.