Honestly, the term can mean several things. There are many loose translations that will be explained later in this answer. However, first off, you should realize that you've spelled the phrase incorrectly. The correct spelling is Chhammak Chhallo.
The phrase is Hindi, one of the most common languages spoken in India, and has received an incredible amount of attention thanks to social media and questions such as yours.
The spotlight was first shined on the phrase when Akon, a Senagalese-American R&B performer recorded a song called Wanna Be My Chammak Challo for upcoming release by SRK's big Diwali, Ra.One. The song, which was supposed to be a shock to the airwaves, was leaked early to the internet and quickly became viral. It became a major topic on Twitter and received an incredible number of hits on YouTube! It wasn't even the final version of the song that made the rounds online and has still inspired all this curiosity.
Like most popular culture and slang terms, Chhammak Chhallo can have several derived meanings, not all of which are terribly positive.
• Chhammak can mean: Bright, colorful, shine, shiny, flashy, extraordinarily bright and colorful clothing, or any number of other derivations.
• Chhallo can be translated to mean: Go, let's go, girls, fast or easy girls.
The less positive derivations on the phrase can be found in both Hindi and Urdu. They are pointed at women who are loose, trashy, too flashy in appearance and too sexual in their depiction of themselves, including their dress, makeup, color and style choices and their demeanor.
The more positive translations of the phrase can be construed as 'beautiful girls,' 'lovely girls,' 'shining girls.' These translations draw up images of women decked out in colorful, sparkling 'traditional' garb rather than more contemporary and less culturally acceptable clothing and styles.
Essentially, in the song though, it is very likely that the hidden - or not so hidden - meaning is 'Do you want to be my sexy/easy/flashy go-to girl?' or something quite similar to this.