OK. This is intriguing.
First up, we need to stop McGovern from getting the nomination, both now and in 1976. Any other liberal candidate would be anathema after McGovern, especially just four years later. And we need a big portion of his support to flow to Chisholm in 1972.
Second: she needs a higher national profile. This is easier in 1976, especially if she wins a large share of the vote in '72, but it could probably be done in 1972. But a '76 win is easier.
So, here's how she could win in 1976:
Sunshine in America: Chisholm '76
-Shirley Chisholm declares for the nomination early in 1971, as opposed to her late entry in OTL, and campaigns energetically in early states, especially Florida.
-Due to butterflies, Peter Sheridan, a heckler, does not confront Muskie on the 'Sunshine Express' in his doomed campaign in Florida. Press coverage of this would have distorted the whole campaign. This allows Muskie to remain more viable in Florida than in OTL.
-Wallace wins Florida with 29% of the vote, with Muskie placing second and, in a shock finish, Chisholm narrowly edging Humphrey, who did not openly campaign, based upon high black voter turnout (as a result of her extensive campaign in the state). This result knocks McGovern, Lindsay and Jackson out of the race, and weakens the Wallace campaign. Muskie becomes the frontrunner.
-In the next major primary, Wisconsin, Chisholm finishes third with 18%; Muskie wins. Wallace matches this with a victory in Pennsylvania based upon support from working-class whites; the two trade primary victories for the rest of the process. Chisholm wins Massachusetts.
-Chisholm wins Maryland in May. Wallace, seeing little prospect for victory in the state, does not campaign there, and hence is not shot. She wins overwhelming support from middle-class liberals and from black voters, and wins caucuses in the South.
-At the convention, 1507 delegates are needed for victory. Wallace has 1100, Muskie has 800, and Chisholm has 450, with the rest scattering. The other candidates pledge to support Muskie in a 'stop Wallace' movement; however, Chisholm extracts a bargain of pledged support in 1976 or 1980 from the party machine.
-Muskie's chosen running mate, Thomas Eagleton, is revealed to have suffered from psychiatric problems. He loses heavily, 55-45%, to Nixon. A Texas congresswoman, Barbara Jordan, loses re-election.
And the rest can be more or less figured out from there for 1976...Chisholm, assigned a seat on Judiciary, plays the Barbara Jordan role, runs as a liberal outsider, establishes party support, and, importantly, establishes as the lead figure in a renewed 'stop Wallace' movement in 1976, allowing her to clinch the nomination. And so forth.
The rest can be left to someone else.