I've had a problem like that on my klx. Doing the valve adjustment didn't fix it, and the chain looked fine. After looking around for a while, I noticed that the timing chain tensioner had some wear on it. The piston that extends out of the tensioner has a row of teeth on it, and a simple catch mates with those teeth when the piston extends to keep the chain tight. One side of the row had worn down and was allowing the catch to release, letting the chain loosen up.
A new tensioner was the end of that noise in my case, but a new tensioner seems to last only a year or less. It seems to me that the part is not designed well. The piston fits sort of sloppyish, and can rotate a bit in the tensioner housing to the point that the catch only touches the side of the teeth and wears it down. It's easy to pull the tensioner out so take a look at yours, and also check with the guys at
www.planetklx.com