Born and raised in Oatley, New South Wales, Kachoyan holds a BA (Media and Communications) from the University of Sydney (including a year at the University of Toronto) and a Master of Arts (Advanced Theatre Practice) from the Royal Central School of Speech and Drama. He completed the National Institute of Dramatic Art Playwright's Studio in 2004.
From 2007 to 2011, Kachoyan was based in London, where he cofounded IronBark. On his return to Australia, he was director in residence for Bell Shakespeare (appointed 2012) and the Critical Stages Resident at the Seymour Centre (appointed 2013). In 2014, his adaptation of The Winter's Tale was directed by John Bell at the Sydney Opera House, and Kachoyan served as assistant director to Simon Phillips on Joanna Murray-Smith's Pennsylvania Avenue for the Melbourne Theatre Company.
In 2018, he collaborated with independent theatre companies Essential Theatre and Three Birds Theatre on Enter Ophelia.