I'm looking to purchase an 87 Jeep Cherokee from an owner and he says that it has a vacuum leak somewhere. It idles rough when it starts up and dies when you first start it up. Asking for $1500 ob

If the start and run fine are on cold starts, I would look for vacuum leaks. The normal start mode for these things is to have a richer condition upon a cold start. When the ECU detects warmth in the engine is drops the extra rich cold start mode then the idle goes rough due to the normal mixture being too lean due to a vacuum leak. Look for cracked, loose or broken vacuum hoses. It could also be due to a EGR valve stuck open.

Look for a vacuum leak at the intake manifold. Spray (flammable) brake clean around the area while the engine is running and look for the idle to change. Also check for a vac leak at the brake booster by pinching the Vac supply line and see if the idle changes.

check for vacuum leaks,the throttle position sensor and the map sensor to see if they are working correctly.

THROTTLE POSITION SENSOR, easy to change and will cause this problem. mounts to intake. If that doesnt work, replace the idle air control solenoid. You can also replace the crank and cam position sensors later if you still have issues,

It sounds like you have a large vacuum leak somewhere. Has any work been done recently to the engine? Perhaps a line was left off. Check closely for disconnected or broken vacuum lines.

Check any rubber hose pieces between the PVC valve and the motor (intake). Normally a leaking hose will have a soft squishy area in the hose where the rubber is melting and the hose will create a vacuum leak at that point. You can tape over the squishy area with electrical tape (get it tight) and if it runs better you should replace the hose pieces. This leak will cause the motor to run very rough at idle, can cause the motor to race when starting it, can cause the vehicle to shift hard (when motor surges) and can throw scan codes indicating Lean Bank 1 AND Lean Bank 2 (presence of both codes is good indicator that vacuum leak is the cause).

SOUND LIKE INTAKE MANIFOLD VACUUM LEAK OR VACUUM HOSES VACUUM LEAK.ALSO DIRTY FUEL INJECTORS WILL CAUSE THAT PROBLEM YOU DESCRIBE.

check for vacuum leaks and make sure throtlebody plate is clean, use throtlebody cleaner and an old tooth brush to clean, if problem is still there then replace the valve (idle air control valve ).

Timing belt could have skipped a tooth.

Horrible vacuum leak could have started. Listen for suction noises when you raise the hood.

Someone could have poured sugar in your tank.

You could have put diesel in your tank instead of gas.

Could be a bad MAP sensor, TPS sensor, etc.

Need more details to be precise.

check timing and set idle to 650rpm