I'd guess the Italian pronunciation as it was invented by an Italian chap called Gigli.
I'm sure someone here will know, though and will be able to write it so that you can tell how to pronounce it.
I'd go for Jeelee with a bit of a sh sound on the J .
From my memories of learning Italian (a long time ago), "gi" is pronounced like the "g" in "generous" and "gl" is a "ly" combined sound with the l slightly ahead of the y. So, Gee ly ee. There or thereabouts!