Could be lots of things that I will list below.

At that mileage, it may be valve train wear, or the timing chain could
be worn and making the noise.  If that slips more than a couple of teeth
or breaks, there will be expensive damage.  You need to determine if
that is the problem.  I don't known if there is a way to determine that
without going into it in which case, with this mileage, if you do go in,
you might as well replace the chain, guide, tensioner, and water pump.
Several hundred dollar job.  (One philosophy might be to avoid the
expense and sell it now, or take your chances and drive unless and until
it self destructs - then make the decision to sell or junk it or replace
the engine at that time.  I see over on wwww.dodgeintrepid.net forums
that 2.7L cores are selling for $400 - high demand due to sludge related
self-destruction).

Also, as you may know, this engine is prone to sludging under less than
ideal conditions.  However, since it has gone this long, yours seems to
have done OK without serious sludging (probably highway miles combined
with good routine maintenance).  The noise may be due to some dirt or
clogging of a valve lifter (lash adjuster).  I would do a controlled,
gradual cleanout by doing an oil change and putting 1/4 qt. of Marvel
Mystery Oil or Sea Foam in the crankcase.  Change oil and filter again
at 1000 miles , again adding 1/4 MMO or Sea Foam.  Repeat again at 2000
miles, then again at 3000 miles.  Continue with oil and filter changes
every 3000 miles.  Notice filter gets changed and MMO or Sea Foam gets
put in at every oil change.  Do not use a "sudden" Rislone type flush.
Doing so could release 160,000 km's of accumulation and prove fatal to
the engine.

I will say also that on the www.dodgeintrepid.net forums I have seen
many similar complaints in which it was eventually reported by the OP
that a worn serpentine belt or tensioner mimicked internal engine noise,
and that replacing one or more of those items got rid of the noise.

HTH.

Bill Putney
(To reply by e-mail, replace the last letter of the alphabet in my
adddress with the letter 'x')