You can forget the timing chain as the cause of an intake backfire. It is about as likely as your left-rear lugnuts to cause that problem.
The causes of such a malfunction are typically as follows:
1. Combustion pressure and gasses entering the intake due to a misadjusted or burned intake valve.
2. Crossfiring ignition due to crosswired or deteriorated ignition leads or distributor cap.
You need a vacuum gauge and a compression tester to diagnose this, starting with a vacuum gauge ($20 at your local parts store). Take a vacuum reading at idle if it is rock steady the problem is likely ignition related. However, if the vacuum reading is not steady, dipping rhythmically, you have #1 above. Sorry, but my money is on this.
Does the engine have a miss? Does it just spit back once, bog, and then accelerate smoothly or does it go pop-pop-pop and buck while accelerating, popping harder with more throttle?
Start with the obvious stuff like valve adjustment and ignition tune-up.
If you have a miss, you can isolate the missing cylinder by removing one spark plug lead at a time. The one which doesn't make the engine run rougher is your leaking cylinder. Remove the plug from that cylinder and test drive. If the pop is gone, pull the head, you need a valve job.