MALAYSIAN CHINESE OR CHINESE MALAYSIAN?

First and foremost, I'M A MALAYSIAN.
But sometimes, I've to state categorically that I'm a Malaysian
Chinese particularly whenever foreign visitors coming to my
shop somewhere in downtown asking me directly:'Are you
Muslim? Or Are you a malay?
So I gotta say I call myself 'Malaysian Chinese' as I'm FIRST a
Malaysian then CHINESE but the writer from Sin Chew Daily
(see post below ) categorized Chinese in Malaysia as 'Chinese
Malaysians'
'So what's the difference?' , asked my buddy, John
"Ah, you caught me there, John" I replied, trying to figure out
' Malaysian Chinese or Chinese Malaysian?
I dunno about you readers but to me, when ask about my
nationality, normally I say something along these lines
I'm a Malaysian, oh I'm Chinese. Malaysian Chinese.
Incidentally, more often than not, I've to declare that I'm a Chinese
simply becoz I do look like a malay!
To say that you're a Chinese Malaysian, sounds a bit of racism
to me but then again I'm not too sure , Chinese Malaysian or
Malaysian Chinese?
Anyone?