The CKGS website says OCI + Renunciation can be done together, but the application widget does not show the renunciation part anywhere in the process. Called CKGS and also emailed them, and reply for both was to apply Renunciation and OCI separately for Chicago. The website will be updated soon.
Renunciation was quick - only three business days. Here is the time line:
10-JAN-2019, Thursday
- Application Received at CKGS
- Application Verified & Processed at CKGS
- Application In Transit to Consulate
11-JAN-2019, Friday
- Application Under Process at Consulate
- Application Reviewed by Consulate and In Transit to CKGS
14-JAN-2019, Monday
- Renunciation Certificate received by CKGS
- Renunciation Certificate picked up by Fedex
15-JAN-2019, Tuesday
- Renunciation Certificate delivered by Fedex.
Applied for OCI after receiving the Renunciation Certificate.
17-JAN-2019 - OCI Application received at CKGS
27-FEB-2019 - New OCI Card picked up from CKGS by FedEx
Total turn around time was 41 days (17-Jan to 27-Feb). Complete time line here -
https://www.immihelp.com/experience/373901-Chicago-New-OCI-card-after-Renunciation.html
No issues at all with the process or with CKGS, everything worked as it should. Good service.