The Chongqing airport website is only available in Chinese but, using the drop down menu for flight searches, it appears that it serves mainly domestic flights:
http://www.cqa.cn/information/navigate/index.a sp
This is backed up by the FareCompare website, which (apart from Singapore and Seoul) doesn't mention any international destinations:
http://www.farecompare.com/flights/Chongqing_A irport-CKG/airport.html
There are no direct flights from India to Chengdu:
http://www.cdairport.com/cdairport/en_front/ai rportinfo_d.jsp
So it looks as if you'll have to take connecting flights, probably into Chengdu via Bangkok. If you try different departure intervals, on this page, you'll be able to see destinations served from Bangkok:
http://www.bangkokairportonline.com/node/129
They include Delhi, with Air India. So you can take Air India to Bangkok and then Thai Airways International to Chengdu
Chris