You're thinking of "Neapolitan", no doubt. It of course refers things or people from the city of Naples, Italy. I'll let Wikipedia take it from there:

"Neapolitan is a kind of ice cream, or more precisely, of ice cream packaging. The box (or tub, bar, etc.) is divided into three flavors, usually strawberry, chocolate, and vanilla. Other combinations are possible, such as banana/vanilla/chocolate or caramel/vanilla/chocolate). Neapolitan is listed as the third or fifth favorite ice cream flavor in the United States. Neil Armstrong ate some in space in July 1969.

Neapolitan ice cream is so called because it is a variant on spumoni, a three-flavoured (usually cherry, chocolate, and pistachio) ice cream originally made in Naples. Spumoni was introduced to the United States in the 1890s."

http://en.wikipedia.org/wiki/Neapolitan_ice_cream

--Very kind words Jodie44. Thank you.

Napoleon Bonaparte (1769–1821) is usually thought to be the inspiration making France the answer to your question.

However, Italy also claims it as Neapolitan ice cream relating it to Naples Italy.

We know Italy had ice cream before the French so my belief is that it originated in Italy.

This ice cream is often called by both names Napoleon and Neapolitan
which brings confusion for its origins.

Edit: The origins of ice cream can be traced back to at least the 4th century B.C. Early references include the Roman emperor Nero (A.D. 37-68) who ordered ice to be brought from the mountains and combined with fruit toppings, and King Tang (A.D. 618-97) of Shang, China who had a method of creating ice and milk concoctions. Ice cream was likely brought from China back to Europe. Over time, recipes for ices, sherbets, and milk ices evolved and served in the fashionable Italian and French royal courts.

http://inventors.about.com/.../ice_cream.htm

I believe no one knows for sure..thanks for the comments :)

The three color variations, (chocolate, strawberry, and vanilla) represent the three colors of the French flag (blue, red, and white) that Napoleon Bonaparte fought under.

it is actually called napoleon ice cream, not neopolitan like you fuckers say. fuck you and everyone who looks like you.