The Chinook design dates back to the 1960s when IR suppression wasn't a consideration. Look at how both engines are fully exposed on the rear pylon. They're tremendous IR sources. Further, they're on both sides of the pylon that houses critical components like the transmission assembly. A hit there will do a lot of damage.

Back during the heaviest fighting in Afghanistan, I saw some news footage of Chinooks filmed through night vision goggles. Those engines lit up like floodlights. I don't know if it'd be possible to retrofit IR suppression to the Chinook, but it might be possible to reduce their signitures somewhat.

This isn't to say that the Chinook is a bad helicopter. It's perhaps the fastest helicopter in our inventory (just slow to accelerate and decelerate). It can operate with heavier loads and at higher altitudes than most of our helicopters, in part because the tandem rotor design means you aren't wasting a significant percentage of your engine power for the tail rotor. Still, the design has some major vulnerabilities to IR missiles. These might be improved with better tactics, such as flying low and fast to blend in with the background clutter.