LONDON, Oct 24 (Reuters) - When Slaven Bilic took over from Sam Allardyce as West Ham United manager in June, he said one of his ambitions was to lead them into the Champions League for the first time.
As West Ham have never finished higher than fifth in the Premier League, not many took him too seriously.
But with a quarter of the season gone, West Ham, in the words of their club song, are bubbling along nicely after adding the scalp of champions Chelsea to those of Arsenal, Liverpool and Manchester City.
In their final season at Upton Park before moving to the Olympic Stadium, West Ham have made their best start to a season since 1983 as they are currently third in the standings.
Striker Andy Carroll, who came off the bench to head the winner in Saturday's 2-1 victory over Chelsea, credited Bilic for the club's run of form.
"We've got a great atmosphere at the training ground. He's a top manager -- he analyses the opposition and then tells us how to beat them," Carroll told the BBC.
"We thought we could beat them today. It wasn't about Chelsea, it was about us.
"We've had some great wins this season and hopefully we'll carry on. The way we're going, we've got a right shot at it. I don't see why not."
West Ham started the season with a 2-0 win at Arsenal and have won four of their five away games, including a league win at Liverpool for the first time since 1963.
If their home form reflected their away form they would be top because Saturday's win was only their second at Upton Park in five games.
"A win is a win it does not matter if it is home or away," Bilic said.
What he seemed most pleased about was that Carroll, who has been ravaged by injuries, looked so sharp after he came on and scored the winner.
"We changed the schedule and philosophy and the way of training," he told BBC Sport.
"He always used to come back after five or six weeks of training but it doesn't help him. He goes running into the box and fighting with people. Now he was training hard for six to eight weeks and came back in the team gradually.
"It's impossible to mark him in the box. His quality was never in question. If he's in good shape now we have a good chance that he will be injury free for a long time. In that case West Ham and England will benefit from that a lot." (Reporting by Mike Collett, editing by Pritha Sarkar)