The humble forward, who died at the age of 83 this week, scored the winning goal in Lisbon as Celtic won the European Cup in 1967.
And Gers supporter Donald McCrorie took to Twitter to share his memories of Chalmers, writing: “I am a Rangers fan - always have been and always will be - but I will never forget what Stevie Chalmers did for my family and my uncle Brian.
“Brian was born with an incurable illness and wasn’t expected to live past five years of age. He lived until he was 17, he was Celtic-daft, and Stevie Chalmers was his hero.
“Brian would write to Stevie every week and Stevie - rather than reply - would visit him both at home in Ochiltree and in the hospital when he was going through tests and when he was poorly.”
Donald posted a photograph of his uncle in full Celtic kit, adding: “The photo is of Brian outside his back door with Stevie’s European Cup-winning shirt and shorts from the 1967 final.
“Brian also received hand-signed photographs from all the Inter Milan squad wishing him well as he fought his illness.
“When Brian passed away aged just 17, Stevie was the first on the phone to my gran and grandad to pass on his condolences.
“Stevie then came to my uncle Brian’s funeral with a wreath from Celtic FC. I wasn’t born to witness all this - I wish I was, but I will cherish the stories.
“Stevie, you were a star to my family and will always be remembered. May you rest in peace and I hope you can enjoy another kickabout with Brian up in the football fields of heaven.”
Chalmers etched his name into Celtic folklore when he scored the decisive goal in the Lisbon Lions’ 2-1 victory over Inter Milan.
A statement from his family, issued via the club, read: “It is with great sadness that we announce the passing of Stevie Chalmers, our loving father and devoted husband to Sadie.
“The Celtic legend was surrounded by family when he sadly passed away early this morning.”
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Chalmers had been suffering from dementia in recent years. His death comes a week after Billy McNeill, captain of the Lisbon Lions, also died.
The statement added: “In recent times Stevie endured the toughest of battles, but just as he approached every game in a green and white jersey, he tackled his long-term illness with much bravery and dignity.”