OK Val, cool story. Things escalated from there, though, with Kilmer declaring that he's been dreaming about the married mother-of-four of late:
A whole day later, Val was back at it, continuing on his new favourite topic: gushing about Cate Blanchett. "She's just as amazing in person," he wrote. "Cate is so real it's almost unreal."
Kilmer went on to reveal that he once took a cameo role in a project (presumably The Missing, in which he played a supporting part alongside Blanchett's lead) just to work with her.
Only problem: He was so "dazzled" by her shovel-handling skills (yes, really) he completely forget his lines.
Kilmer's next tweet: A black-and-white shot of Blanchett, accompanied by a musing of his own: "I mean even if she couldn't act you know what I mean?"
Yeah Val, we know what you mean.
At this point, some on social media felt it necessary to step in. 'Val,' they tweeted. 'She's a married woman. You're coming off a little intense. You don't have to share this all on Twitter. Maybe buy a diary.'
Kilmer was having none of it, hitting back at one person who'd labelled his tweets creepy: "Nothing in the least creepy about loving someone. What kind of world do you come from?"
He's got a point: We wish we loved anything quite as much as Val Kilmer loves Cate Blanchett.
And while Blanchett doesn't have a Twitter account, if she - or perhaps her husband Andrew Upton - find Kilmer's tweets cause for alarm, fear not: He's moved on to Jessica Chastain now.