PoD needs to be earlier, and has to do with the mindset of the Republican Party. Chafee is, for the Republicans, a Rockefeller. For him to even be considered for the Nomination, you'll need the Republican Ideology to be in the 'Moderate-Liberal', whilst the Democrats 'Conservative'.
To do this, while we can do PoD's closer to present, I'm going to go to my extreme and postulate that Nixon wins in 1960 (Chafee was born in '53, and came from a family of politicians, so him being one under this condition isn't unlikely), and starts pushing Civil Rights (Nixon having been supportive of Civil Rights). This results in Conservative Republican's who oppose the movement flocking to the Democrats, who take position as the opposition to the Republican support, resulting in them becoming more Conservative. Eventually Chafee wins nomination in a liberal-Moderate Republican party in 1996/2000/2004, and becomes President (assuming he doesn't die or join the Democrats).
Basically what I'm saying is that for Chafee to become President, you need the Republicans to be ideologically moderates. I know I could probably pick more recent (Reagan wins in '76, looses in '80, and the Party drifts from Conservative to moderation in he hopes this will have them win), but that was the first thing that came to mind.