Je te tiens, tu me tiens, par la barbichette;
Le premier qui rira, aura une tapette!

"I hold you, you hold me, by the chinny-chin;
The first to laugh, will have a little slap!"

A French kids' game. Two children face each other eye-to-eye and grab the other's chin. Whoever laughs first gets a (playful) slap on the cheek. Barbichette literally means "goatee", but children use it much like "chinny-chin" is used in English. The word tapette can mean "flyswatter" or "carpet beater," but because it is also a vulgar word for a homosexual, many children have learned the rhyme with the word giflette ("little slap") instead. The last "-te" of each line is pronounced, unlike standard spoken French, but common in French poetry.

I've always heard it with a specific meter:

1  &    2       3   &   4       5   &  6     &    7-&   8 (*)
Je te   tiens,  tu  me  tiens,  par la barb- i-   chet- te
Le pre- mier ,  qui ri- ra   ,  au- ra une   tap- et-   te

A quick search on the Internet informs me that there's another line that's sometimes said: de nous deux ("of us two") is sometimes inserted between premier and rira, although I don't know how that works into the meter.

* Beat notation: each number is a down beat (eighth notes in this case); the ampersands are the up beats. It's a common drum notation; see 1E&A. The "7-&" means the syllable is held until the up beat after 7.