In my experience, the timing chain usually lasts as long as the rest of the motor (200-300k miles). If you suspect timing chain issues, I agree you should start with the tensioner. Its pretty easy to diagnose with the valve cover off. You can pump it up manually with a screwdriver and see if it holds pressure. If not, replace it. Just make sure you fill the small reservior with oil and pump up the new one. If its pumped up and the chain is still loose, then the chain may be stretched beyond the limits of the tensioner.
If its an old motor and you just want to keep it running on the cheap, you can actually replace the chain and cam gear without removing the lower timing cover. You just remove a link from the old chain, attach the new chain and rotate the motor over (by hand!) until the new chain comes through. It usually takes two people -- one to keep tension on the two ends of the chain and one to turn the motor -- but I've managed to do it solo. Make sure you line up the upper timing mark before you loosen the chain -- it'll help getting it timed again.
HOWEVER, if you're going to go to the trouble of replacing the chain, then you really should replace the tensioner, guide and rails. They do wear out and get grooves in them. That does require removal of the front cover (as stated above). Don't even try to get the lower timing gear off without an industrial strength gear puller. I'm pretty sure that can't be done with the crank still in the motor -- I've tried several times and gave up every time (both with the motor in and out of the car). Even if you do manage to get it off, the new one must be super-heated and pressed on -- not something that can be done with the motor in the car -- not to mention you need to remove the oil pump (or the pump chain) -- which is a whole 'nother can of worms. . .