Once the paperwork, photos and fingerprinting were all submitted, it too about five agonizing weeks as I recall. It took my father about two weeks to receive his CHL prior to the switch for electronic fingerprinting. I took my CHL course the first month that the state required electronic fingerprinting submissions through L3. As I understand it, going through L3 for the fingerprinting actually slowed DPS down in processing when I took the class because DPS was backlogged initially. Good luck!
It took them about 3 weeks to figure out that I was born overseas and request a scan of my passport, but the letter said they would try not delay the process too much. I returned the information requested in a few days and the total time was about 45 days. I am pretty sure you can track the progress online if you have your paperwork with the tracking numbers.
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