TCM was showing this as part of their "Oscar" month. I ended up staying up late to watch it.

Wow, what a waste of time! The problem isn't KC or WH or their chemistry (or lack thereof), but the idiotic plot that just doesn't make any sense. I could fill pages with examples, but the one that made me really sorry that I had sacrificed my beauty sleep to watch this was when Costner's character dives into a freezing lake to knock a kid out of a boat, but for no apparent reason other than he just figure out that the bad guy is nearby. After safely out of the water, the boat stops in the middle of the lake and blows up. Since neither Costner or Houston's characters had been in the boat or shown any interest in the boat, the whole idea that someone would try to kill them by blowing it up made absolutely no sense at all.

And what about the ridiculous attempt at romance, which is obviously the whole point of the film? There is not one credible scene that explains either character's attraction for the other. None. So, the reason for no chemistry between the two is that the idiot who wrote this didn't provide any dialog or staging to provide them with any motivation.

So, my advice is to buy a Whitney Houston album so you can hear her fabulous voice without interference from all the foley noise, and then rent "No Way Out," which provides all sorts of motivation for the romance and sex scenes with an equally serious, but far more plausible performance from Costner.