Wow, I had no idea there were so many versions! Here's how it was sung to us as kids:

There was a Chinaman; lived in Japan
His name was Chickala Chickala Chan
His legs were long and his knees were knocked
And this is the way the Chinaman talked
A chickala chee chileye chilo
A chickala Romeo and a banana go
Walaka walaka chance to see
In a banana go alchio

The Chinaman he did up and die
and in his coffin he did lie
They sent him back to old Japan
and this is the way his epitaph ran
(Refrain)