Jon Hamm -- Hey Ethan Hawke, Back OFF My Old Lady

Jon Hamm just proposed to a Hollywood icon ... and she's more than twice his age.

Hamm ran into Academy Award winning film editor Anne V. Coates Wednesday night at Chateau Marmont and couldn't stop gushing over her work ... she's the cutting room genius behind a ton of classics, including "Lawrence of Arabia."

When he got down on one knee to shower the 89-year-old with praise it got real ... the entire restaurant shouted, "Proposal!" ... so he hammed it up, took her hand and asked her to marry him.

Unclear if she said yes ... but when Hamm left, an equally starstruck Ethan Hawke swooped in and got pretty handsy with her himself.

It's not good to toy with emotions, boys ... especially at her age.