The club's billionaire majority shareholder Stan Kroenke is one of a new generation of foreign owners who have bought into the game in Britain, but while some of them have spent with abandon to get results on the field, Kroenke expects the club to stay true to sound financial principles.
The order to control the purse strings didn't stop Chapman entering club folklore, leading Arsenal to the first of 13 league titles, making it the most successful team in England after Manchester United and Liverpool, but the trophy cupboard has been bare for several years.
Arsenal, nicknamed "The Gunners" after the munitions factory workers that founded the club in 1886, last won the English Premier League in 2004 and lifted the FA Cup in 2005. They have won nothing since, and supporters who pack the plush Emirates Stadium, the club's home since 2006, want a better return on some of the highest ticket prices in English football.
Even the annual consolation of a place in the Champions League, worth around 30 million pounds, could slip from its grasp. The top four from the Premier League qualify for the competition, and Arsenal is currently fifth behind local rivals Tottenham Hotspur.
Frustrated fans say the club is the victim of a lack of drive and investment by Kroenke, who took control two years ago in a deal valuing the club at 731 million pounds.
Those who work for the 65-year-old Kroenke, who owns sports teams on both sides of the Atlantic, dismiss claims he is out of touch with English football and its passionate fans.
"He understands sports. He understands Arsenal," club Chief Executive Ivan Gazidis said in an interview.
"The guy I know is phenomenally ambitious for this football club and has given it support at every possible level," he added, saying Kroenke comes to London every month.
FANS BLAME BOARD
While the Americans who control Arsenal, Manchester United and Liverpool have tried to run the clubs along business lines, clubs like Chelsea and Manchester City have muscled into the Premier League elite over the past decade thanks to hugely wealthy owners from Russia and Abu Dhabi who have been prepared to underwrite their financial losses.
Arsenal fans who have seen their club overtaken by these newly rich teams believe "Silent Stan" should do more.
"There is not enough energy or ambition to push the club hard to go forward," said Tim Payton of the Arsenal Supporters Trust (AST), a lobby group of fans who own shares in the club.
"Kroenke owns the club, but he's out of the country, and most of the rest of the board are over 70. It does feel that coming fourth is the height of ambition rather than the minimum requirement," he added.
Gazidis, 48, believes Arsenal will soon benefit from the completion of a financial transformation that began with the move to the 60,000-seater Emirates Stadium from their former home at nearby Highbury in North London.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.