At the end of a fiercely contested match, Hornets captain Jack Brivio’s effort was the decisive miss as Jamie Yila slotted home the tenth penalty to give the Chats a 4-3 victory after it had ended 1-1 at the end of 120 minutes.
After a goalless 90 minutes, Kareem Isiaka fired Chatham in front on 106 minutes – but Horsham struck back six minutes later through James Hammond.
And after a tense period of extra time failed to find a winner, it was on to penalties.
The Hornets missed two of their five spot kicks, with Jack Mazzone and Brivio both failing to convert.
Hammond, Danny Barker and Lewis Carey scored for Horsham, but Chatham were almost perfect from the penalty spot.
The Hornets’ attentions now turn to a historic Sussex Senior Cup final against Hastings United at the Amex on Wednesday, May 8.
See some of John Lines’ pictures from the game on this page and the ones linked. You can read Horsham manager Dominic Di Paola’s thoughts in the West Sussex County Times, out every Thursday.
1. Horsham FC suffer penalty shootout heartbreak as Chatham clinch place in play-off final - the match in pictures
Action from Chatham v Horsham Photo: John Lines
2. Horsham FC suffer penalty shootout heartbreak as Chatham clinch place in play-off final - the match in pictures
Action from Horsham v Chatham Photo: John Lines
3. Horsham FC suffer penalty shootout heartbreak as Chatham clinch place in play-off final - the match in pictures
Action from Chatham v Horsham Photo: John Lines
4. Horsham FC suffer penalty shootout heartbreak as Chatham clinch place in play-off final - the match in pictures
Action from Chatham v Horsham Photo: John Lines