The record set by the Scottish side is on the verge of being broken... by the same team.
Brendan Rodgers' Celtic side won 3-0 at Aberdeen on Wednesday night to extend their unbeaten domestic run to 61 consecutive matches.
This means they are just 90 minutes away from breaking the record, previously held by Willie Maley's Celtic side in the early 20th Century.
The Hoops face Kilmarnock at home on Saturday and can break the century old record if they avoid defeat.
Ahead of the match, Rodgers was asked about the possibility of setting a new record.
"I wasn't aware of that. We've always focused," he said. "The only time this was mentioned was when the record was 26 and there was a bit at 23, 24 and could we beat it?
"Once we got over the line we focused on the next game. To have no complacency and to win.
"That's what they've done. It's an incredible credit to the players and staff for the mentality to work like that.
"We come back in the early hours from games and they want to work the next day.
"I give them a free day but they come in. It tells you about the winning mentality and how hard they're working."