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harryBud Fowler is generally considered the first Professional African-American player. Don't remember which team he played for, but it is now not considered a part of a "Major" (National, Union, American Association, American, Federal, etc.) League. I think that he played in the late 1870's.
Moses Walker is generally considered to be the first African-American to play in the Major Leagues. I believe that he played with Toledo of the American Association in the mid 1880's.