It was the spring of 1987, and the Clarets needed to beat Leyton Orient in the last game of the season to retain a chance of avoiding relegation from the old Fourth Division.
A capacity crowd of more than 15,000 supporters packed into Turf Moor as Burnley defied the odds to beat the promotion-chasing Londoners 2-1 and condemn Lincoln to the drop.
Lifelong fan Kilby attended the game as a supporter, before joining the board of directors and becoming chairman over a decade later, and will be full of pride on Monday when his club face Sheffield United in the Championship play-off final at Wembley.
The famous old Lancashire outfit have come a long way since their flirtation with oblivion 22 years ago.
Kilby, a highly successful businessman, said: "To be here and on the threshold of the Premier League shows how far the club has recovered from that absolute low point in 1987.
"I was at the Orient game as a supporter and even now when I watch a dvd of the game I still have tears in my eyes at certain points.
"But it was something that woke up this town. It didn't want to let this club go.
"Now to progress this far, and get this close to returning to
the top flight, is proof positive that Burnley Football Club is something that people believe in."
That belief has been strengthened by the Clarets' excellent manager Owen Coyle, who has made his side a force to be reckoned with this season.
Coyle's men dumped Fulham, Chelsea and Arsenal out of the Carling Cup and came agonisingly close to overcoming Tottenham in an epic semi-final encounter.
The success has been achieved on a shoestring budget and with one of the smallest squads in the Championship, making Coyle one of the hottest managerial properties outside of the top flight.
The former Bolton striker has won many admirers since arriving from St Johnstone in November 2007 and keeping hold of him could prove difficult.
"You are always open to that," admitted Kilby.
"He's done extremely well on a limited budget, that's what makes his achievement stand out I think.
"I think Owen would love to be manager of Burnley in the Premier League, pitting his wits against the big boys, and why not?
"But just for Burnley Football Club to even be talking in those terms is absolutely fabulous.
"Either way, Owen is destined to be one of the top managers in the game."
Kilby admits that reaching the top flight for the first time in 33 years, and the estimated £50million reward, would provided untold benefits to the club.
He explained: "It would be like an atom bomb going off in our finances.
"It could easily set this club up for many many years to come.
"We could do all sort of things to secure our future and the money would transform us beyond recognition."