This variant is described in A Gamut of Games by Sid Sackson (Pantheon Books, 1982). Knight Chase is played on a standard 8x8 chessboard with only 2 Knights and a supply of 30 markers (stones, poker chips, buttons, cardboard chits, etc.).
Black moves first.
A move consists of a normal Knight's move plus the placing of two markers. One marker must be placed on the square the player's Knight previously occupied. The other may be placed on any unoccupied square. Below is an example of a first move for Black:
Markers occupy their squares, prevent either Knight from moving onto (but not leaping over) the marked space.
White wins by capturing the Black Knight. Black wins by avoiding capture. After the thirtieth marker has been placed, White is only allowed ten moves in which to capture the Black Knight. Otherwise Black wins.
If either Knight is unable to move to an unmarked space, Black also wins.
Black to move. At this point Black cannot avoid capture.