The version I learned from my grandmother goes like this:

Once there was a Chineseman
His name was Chikka Rakka Chi Chai Cho
His feet were long and his arms were short
This Chinese man couldn't walk nor talk

Chikka Rakka Chi Chai Cho chikalera
Bungalera piggy wiggy waggle
Ogo pogo anna banna coco
Cheraby cheraby chi chai cho

This Chinese man, he had a wife
And oh, they lived a terrible life
She cut off his pigtail, it was too long
And sold it for a Chinese song

Chikka Rakka Chi Chai Cho chikalera
Bungalera piggy wiggy waggle
Ogo pogo ana bana coco
Cheraby cheraby chi chai cho

It was always accompanied by a lot of clapping. I always thought she had made it up, so I'm happy to know that there are other people out there with their own versions of it. Makes me feel less crazy somehow :)