I had this very issue, after approximately 10-15 minutes (depending on temp), I could hear a relay under the hood clicking. Then I could start the Jeep when the CEL came on.
It ended up being the capacitors in my ECU. Don't think buying a replacement ECU will fix this, I bought a replacement and it had the same problem. I swapped out the capacitors with brand new ones and now it fires up instantly no matter how cold.
Read through this link, has great troubleshooting and a pic by pic on how to do it yourself. Took me roughly an hour to swap the capacitors, including smoke/beer breaks.
Crash Course In Brain Surgery Replacing Capacitors On ECU - JeepForum.com