Yes, it has racist connotations, but there's a history of misunderstanding over the word:
http://en.wikipedia.org/wiki/Chinky
The problem is with education - people say things and often don't understand how offensive it is (sometimes using words as slang and/or affectionate abbreviation), and sometimes people use a word to incite hatred.
Someone could say "Do you want anything from the Chinky" in reference to a takeaway with no harmful intent, and then someone could shout "Stupid Chinky" to an east asian, which is directly abusive and intentionally offensive.
It's often the same with the whole 'Yid' word. Or even the 'n' word (where, apparently, it's only racist if the person saying it isn't black).
People say things to their workmates/friends to sound 'funny' or 'cool' all the time, I witness it often and it makes me uncomfortable, but I wouldn't say that I thought they were racist, just ignorant.
I shudder when people use the phrase 'coloured' in a conversation with me, but I know for a fact that it's an education problem rather than racism.