Midfielder Cammy Devlin insists Hearts "have done absolutely nothing yet" and is urging fans to get behind the club as they continue to push for the league title.
The Tynecastle club last claimed the top flight title in 1960 and since then Celtic and Rangers have dominated the league.
But Derek McInnes' side are the team to beat this season, sitting two points in front of second-placed Rangers and three ahead of Celtic in third who have a game in hand.
They welcome Falkirk on Saturday and Devlin, currently sidelined with an injury, is urging supporters to turn out in numbers again.
"It's so important that they're with us," he told Hearts TV.
"Whether we're winning, drawing late on or maybe we need them to help us come back into the game. Things can't go your way all the time. When I see them on the street I tell them how important it is to stick with us.
"It's been an amazing season so far but at the end of the day we've done absolutely nothing yet. Come the end of the season we all want the same thing, we're all trying to push in the same direction.
"Hearts are playing the way a Hearts team should look, winning games when we're playing well and winning games when we're not playing so well which is important for a successful team."