When I first heard the rhyme "Gigalo" in the 1980s from my daughter and her friends, I arbitrarily chose the spelling "Gigalo". To date, I've found at least 9 written examples online of this cheer. The spelling that is most often used is "Gigalo" and not "Jigalo". I think that it's important to note that the girls I've heard recite this cheer definitely say "gig-GAH-low" and not "gig-OH-low". And most of the online examples of this rhyme that I have found are written as 'gigalo".

Why is that important? Well, the most familiar definition of a "gigolo" is "A man who has a continuing sexual relationship with and receives financial support from a woman". http://www.thefreedictionary.com/gigolo

I can see why folks might frown upon children chanting about a gigolo.

But feedictionary.com gives a second definition for gigolo-
"A man who is hired as an escort or a dancing partner for a woman."

That online dictionary also provides this information about the etymology of the word gigalo:
"[French, perhaps from gigolette, dancing girl, prostitute, from giguer, to dance, from gigue, fiddle, from Old French; see gigot.]"

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But suppose the name of that cheer is supposed to be "Jigalo"?
Since the word 'jig" is found in the beginning of Jigalo, maybe the one of the definitions of 'jig' might us 'suss' out the meaning of that cheer's title.

http://en.wikipedia.org/wiki/Jig has this information "The jig (Irish: port) is a folk dance type as well as the accompanying dance tune type, popular in Ireland. It is sometimes seen in its French or Italian forms, gigue or giga, but these are more usually used for the baroque dance forms".

-snip-

Hmmm...Notice the 'gigue" or "giga" words. Very interesting.

But suppose Jigalo or Gigalo is actually supposed to be written "Jigalow" or "Gigalow"? Could this word mean "Dance low"?
Meaning "shimmy" or dance some other step moving from an upright position to a position close to the floor?

We may never known where the cheer Gigalo came from. We also may never know the true meaning [if any] of the word Gigalo, Jigalo,
Gig-olo-oh,Jackalow, and/or other similarly spelled words.

But at least we have another theory for that word's meaning besides
"a man who has sex with and is supported by a woman".