Another Chase fan here. Just after I arrived in Ireland for a two-week vacation this past May, I get a notice from Chase that they're canceling my card due to (actual) fraud and sending me a new one. Except that I was depending on the Chase card while I was in Ireland. Their CS was extremely helpful and suggested a setup where they'd authorize card-present transactions while I was in Ireland but block others (unless I explicitly authorized them.) (And then I was embarrassed when my card was declined in Ulster, but that was my fault because I wasn't in Ireland anymore - and they had asked what other countries I would be in.)
American Express has also been good about fraud detection and alerting me instantly, though on a previous European trip I noticed a whole slew of bogus charges to my card using a number that had been canceled two cards ago. Their explanation was that if it came through a processor that had done a valid transaction before (which had been the case), they'd let it go. No big deal to get it taken care of.