I was amused to see this word come up, since in Spanish it refers to a lady's most private part! And, I was surprised to see, quite a few other coincident meanings. See, for example, http://www.urbandictionary.com/define.php?term=chichi

When I was a boy in the '50s in Mumbai (then known as Bombay), the term 'chichi' I heard sometimes used to refer to someone who was part-Indian, part-European. I presume it was Hindu in origin, but I don't know for sure, and I suppose it may have derived from the 'faecal' (fecal?) connotation mentioned in the Urban Dictionary, suggesting someone dirty and untouchable.
Can anyone elaborate?
Sam

Welcome to you both!

Chichi is also a lump of deepfried batter lightly sweetened and sprinkled with sugar. For the children a traditional "can we have a chichi? " - item on village fairs in the Provence/ Bouches-du Rhône.
Froufrou is a dutch biscuit. Two small thin rectangular wafers with a thin layer of vanilla sugercream in between. Yum!

ChichE (with an "e" at the end) refers to a woman's breast, and that applies to Spanish spoken in Latin America. http://lema.rae.es/drae/?val=chiche

In my country, "chichi" refers to a baby.