Chilton scored 222 goals in 476 appearances for the Tigers between 1960 and 1971 and formed a legendary striking partnership with Ken Wagstaff.
The pair helped Hull win the Division Three title in 1965-66, with Chilton going onto turning down offers from several clubs, including Leeds United and Tottenham Hotspur, to remain with his hometown club.
The fans' favourite, born in the East Yorkshire village of Sproatley, was an inductee into the club's Hall of Fame alongside the likes of Wagstaff, Ian Ashbee, Billy Bly, Chris Chilton Andy Davidson and Pete Skipper.
After finishing his playing career, Chilton worked in a number of backroom roles and gave over three decades of service to City.
Chilton's stint included a spell in caretaker charge of the club, while he was the assistant manager during the promotion seasons of 1982/83 and 1984/85 under Colin Appleton and Brian Horton respectively.
Chilton had been suffering from dementia and Alzheimer's, with the football community having come together to raise more than £40,000 as part of a campaign to help support him and his family to pay for respite care.
A Hull City statement read: "Hull City are today in mourning as we come to terms with the news that the club’s record goalscorer Chris Chilton has passed away.
"Chris, who scored 222 goals in 476 appearances for the Tigers between 1960 and 1971, passed away overnight at the age of 77 and our thoughts are with the Chilton family, and their many friends, at this sad time.
"Club flags will fly at half-mast as we remember a man who was simply worshipped by the thousands that watched him play at Boothferry Park, and whose goal-scoring exploits may never be bettered.
"Chris’s hero status was highlighted recently as the club and supporters helped to raise more than £40,000 to support his care needs during a period of ill health.
"His contribution to Hull City will never be forgotten. Rest In peace, Chris."