I had the same thing happen to my 89.
The person that had it before me tried replacing the mass air unit but the
check light still was on.
( I think this is one reason I got such a good deal on it )
Then I found out in this group what the problem was.The burn off relay and
power relay are right behind the battery
on the firewall.
Called all the local shops here and nobody even new about them. Finally
called the local Chevy dealer and after
explaining to them were the parts were located on the car they now know what
the mass air burnoff and power relays
are!!
They are less than 15 bucks each at the Chevy dealer so I replaced both of
them,and no problems with it so far (3 years).
Hope this helps.
             Mike

No, don't do that.  When you get an engine light, the car computer
goes into a default mode, called "limp home mode".  It retards the
timing and does some other things so the car just runs.  Your mileage
and performance will suffer.

As someone mentioned, it's probably the relays.  I seem to have to
replace mine every other year, so now I buy two of each at a time.
They're not that much.  You can still buy them at the dealership for
about $12 and $18 each (can't remember which one costs what).  Take 15
minutes to replace.  Couple bolts hold them on over by the battery.

Note that after you replace the burnoff relay, it might take a couple
of starts before the code goes away.  The burnoff relay clicks on when
the car is shut OFF.  I've apparently had enough crud on the MAF wire
where it took a couple of burnoff cycles to clean it throughly.