No one being has slain more than a single Primarch, but every Primarch death can be attributed directly or indirectly to the forces of Chaos.
For sure, we only know of 4 dead Primarchs.
Rogal Dorn is supposed to be dead too, but we don't know for sure. And if he is really dead, he died during the very first Black Crusade battling the forces of Chaos.
Everyone else is accounted for or missing.
There's an excellent entry on the Lexicanum that gathers together (what looks like) every mention of the Lost Primarchs and their legions. Definitely worth a read if anyone is interested.
During the events of Prospero Burns, it's suggested that Leman Russ could be responsible for the deaths of both of the II and XI Primarchs:
In a conversation near the end of the novel, Leman Russ discussed the coming destruction of the Thousand Sons Legion. When asked if he was concerned over the fact that Space Marines were fighting other Space Marines, he commented that this was not the first time the Wolves had been called on to perform this task. This might be a reference to the possible destruction of the Legion II and/or XI.
But as is usual for The Black Library, it's left purposely ambiguous.
However, Leman Russ could be referring to when he and his Legion battled the World Eaters during the Great Crusade, or when he fought against Lion 'el Johnson and the Dark Angels.