“Marvolo Gaunt! You-Know-Who’s grandfather! ... Marvolo Gaunt said he was descended from the Peverells! The ring, the ring that became the Horcrux, Marvolo Gaunt said it had the Peverell coat of arms on it! I saw him waving it in the bloke from the Ministry’s face, he nearly shoved it up his nose!”
-- Harry Potter (DH22)
Shortly after murdering his father and grandparents, Tom Marvolo Riddle uses those murders to create a Horcrux from Marvolo Gaunt’s heirloom ring. The ring had once belonged to the Peverell family.
While we don't know exactly when Riddle created this Horcrux, it's likely that the ritual to create a Horcrux would have to take place very soon after the murder upon which it is based. Since we know that Tom Riddle murdered his father and paternal grandparents in the summer of 1942, we can assume that the Horcrux was also created during that summer. Therefore, when Riddle was asking Slughorn about making more than one Horcrux, he was wearing just such a dark magic item on his finger at the time.