He writes (and check out the graph):
Actually, as you can see from the chart above, what happened was this: Chile had a huge economic crisis in the early 70s, which was, yes, partly due to Allende and the accompanying turmoil. Then the country experienced a recovery driven in large part by massive capital inflows, which mostly consisted of making up the lost ground. Then there was a huge crisis again in the early 1980s – part of the broader Latin debt crisis, but Chile was hit much worse than other major players. It wasn’t until the late 1980s, by which time the hard-line free-market policies had been considerably softened, that Chile finally moved definitively ahead of where it had been in the early 70s.
Krugman views this analysis as taking away some credit from Milton Friedman and the Chicago School. Given his recent writings on the Euro, it is odd what he doesn't mention, namely that the Chilean catastrophe of 1982-3 stemmed in large part from a Chilean overvaluation of the currency, rooted in a peg to the rising U.S. dollar. Milton Friedman, of course, recommended floating exchange rates.
It's also incorrect to argue that the boom starting in the late 1980s stemmed from the considerable softening of hard-line free-market policies. More accurately, Chile increased its international credibility by becoming democratic, while showing that elections would likely leave the core economic reforms intact.
You would do better to read my post on the economic legacy of Pinochet. There are significant qualifications to the story of Chile as "free market miracle," but they're not the ones Krugman makes.