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.
"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.
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.
