Stinking Of You features the late Nirvana frontman and his wife singing together on the never-released track.
The song appears on a new documentary about Patty Schemel, former drummer with Courtney’s band Hole.
In a clip from the doco, Cobain, who was never comfortable with the media spotlight he created for himself, hangs out doing regular stuff, such as playing with his daughter, Frances Bean, and eating cake.
Love can be seen playing an acoustic guitar while she and Cobain sing.
Last week former Hole guitarist Eric Erlandson claimed Cobain had recorded enough material for a solo album before his suicide in 1994.
Erlandson said: “He was headed in a direction that was really cool. He was going towards, a solo album but working with different people.
“I was really excited about some of the stuff he was working on. I got to see him play it in front of me.
“That’s why I was really sad when he died. He was cut short. Who knows where this music would have gone?”