"Dear Chris Cornell used to come to my parties n Hollywood n play quietly in the corner until all the woman were literally at his feet listenin," Kilmer wrote. "He was such a great song writer and so humble about it. A real artist. And that voice..."
Kilmer, of course, isn't the only one affected by the loss of Cornell, who died in Detroit following a performance in the city. Fellow musicians, such as Elton John, Billy Idol and Slash, have taken to social media to mourn the late singer.
Cornell's cause of death is still not confirmed at this time. Police are investigating Cornell's death as an apparent suicide, a spokesperson for the Detroit Police Department tells ET. He was 52 years old.
If you or someone you know needs help, please call the National Suicide Prevention Lifeline at 1-800-273-TALK (8255).