Manager Sam Allardyce said West Ham are "breaking barriers" in the Premier League as they head into the Christmas period in a Champions League spot.
The Hammers are fourth in the table after a 2-0 home win against Leicester.
"It's not often a team is breaking the barriers everybody else doesn't expect them to break," said Allardyce.
"Being fourth is a great Christmas present for everybody at West Ham and having 31 points already is a pretty major achievement for us."
Goals from Andy Carroll and Stewart Downing secured a routine win against the Foxes and ensured the Hammers would claim their highest Premier League position at Christmas.
They have not been in a higher position in the top-flight of English football on 25 December since 1985-86, when they were third in the old Division One.
|West Ham have already won nine Premier League matches in 2014-15. They only won 11 in the whole of 2013-14.|
West Ham's best Premier League campaign came in 1998-99 when they finished fifth and their last European football experience came in 2006-07 when they lost in the first round of the Uefa Cup.
If they finished fourth at the end of the season they would enter the play-off round for the Champions League, a competition they have never played in before.
However, with games to come at Chelsea on Boxing Day and then at home to Arsenal on 28 December, Allardyce is not getting carried away.
He added: "You should enjoy the moment and continue enjoying it for as long as it lasts. Hopefully it will last for a good while yet.
"We've sustained our position between sixth and fourth in recent weeks, but the end of January will tell us what we can possibly achieve.
"The players who have applied themselves magnificently well are reaping the rewards."