Nope, I thInk whivsiv just saw the $120m cap in the title.
To answer your question, your chain has to be 25 player long. That chain does not have to be in chronological order. For example- (and I am making this up, not necessarily legit teammates):
John Clarkson played with Ed Delahanty on the 1890 Phillies
Ed Delahanty played with Tuck Turner on the 1894 Phillies
Tuck Turner played with Cy Young on the 1910 Red Sox
Cy Young played with Ox Miller on the 1907 Red Sox
Ox Miller played with Nap Lajoie on the 1901 Naps
Nap Lajoie played with Ratface McGee on the 1914 Indians
Ratface McGee played with Lou Gherig on the 1926 Yankees
Lou Gherig played with Joe DiMaggio on the 1937 Yankees
Joe DiMaggio played with Joe Blow on the 1940 Yankees
Joe Blow played with John Doe on the 1937 Pirates
John Doe played with John public on the 1942 Reds
John Public played with Harry Johnson on the 1947 Reds
Harry Johnson played with Richard Head on the 1946 A's
Richard Head played with Joe Schmo on the 1953 White Sox
Joe Schmo played with Mickey Mantle on the 1956 Yankees
Mickey Mantle played with Seymour Butts on the 1963 Yankees
Seymour Butts played with Itchy Burns on the 1969 Indians
Itchy Burns played with Roberto Clemente on the 1971 Pirates
Roberto Clemente played with Willie Gogh on the 1970 Pirates
Willie Gogh played with Mike Schmidt on the 1977 Phillies
Mike Schmidt played with Pete Rose on the 1980 Phillies
Pete Rose played with Tracy Jones on the 1985 Reds
Tracy Jones played with Ken Griffey Jr on the 1990 Mariners.
Ken Griffey played with Adam Dunn on the 2006 Reds.
There is a mostly fictional chain of 25 guys. That would be your team (season doesn't matter).