I have heard that somewhere in Shas, there is a case of Gilgul neshama mentioned. Is there actually such a case, and where is this to be found?
No there are no explicit sources. In fact Rav Saadia Gaon in Emunos V'Deos explicitly rejects this concept and considers it a non Jewish concept. The Rashash in the back of the gemara in Bava Metziah 107 brings an indication from that gemara against concept of gilgulim.
(This does not mean other do not hold of the concept, in fact many Rishonim ,and even Geonim do ,but a source in Shas is not explicit).