Another bank that will is Hang Seng - but they are very picky with documentation. I went there with a utility bill and a us bank statement - they were rejected because my name didn't match the name in my passport (no middle name). Very frustrating talking to them - their 'front line' is manned by interns and junior hires that can't answer even basic questions.
I noticed there seemed to be a lot of mainland customers in Hang Seng - using their PRC ID card for identification. Strictly speaking I I think they are not allowed to have these accounts (mainland law)?