The act of finding a Chinese hooker, impressing her with lies of you being a cage fighter in Beijing, then taking her up the ass with sweet and sour sauce and make her talk in Cantonese or Mandarin.
Dude, that hooker though I was a cagefighter back in '94. She was so impressed, she let me do the Dirty Chinaman...for free...
If someone says they're going to have a dirty chinese, it means they're looking forward to what is expected to be an immensely delicious chinese take-away.
An Irish saying, it involves the popular misuse of the word 'dirty' as slang for something beyond the realm of every other positive word in the English language.