You can do an engine swap on your 1988 Jeep Cherokee, but you're going to need a smog check referee inspection after the job is complete. While installing the LT1 engine in your Jeep Cherokee you will need to install all the emission components for the LT1 engine as well (including computer ECU and exhaust system, specifically the CATs).
After the swap is complete, your Cherokee will need to be inspected and smog checked by the California State Referee. The Referee will ensure that the job was done properly and that the new engine does not pollute. If all is well they will issue you a BAR label which will be placed on your Oldsmobile Cutlass' chassis which will be an indication that the vehicle is California legal and allow you to obtain subsequent smog tests at ordinary smog stations as opposed to the referee center.
In this case we recommend you speak directly with a State Referee before beginning this project. You can contact them by calling (800)622-7733.