The Hammers take on a Blues side full of confidence following their League Cup final victory over fellow Londoners Tottenham Hotspur at Wembley on Sunday.
Now concentrating on the league, the Blues have a great chance to edge closer to the title and in striker Costa they have the perfect player to help mix it up against a direct Hammers team.
The Brazilian-born scorer has netted regularly during his debut Premier League campaign, but his over-exuberant style of play and clashes with defenders have prompted heavy criticism from some quarters.
Nevertheless, Allardyce feels Costa thrives on the physical battles and has warned his defenders not to get involved in his antics, fearing the former Atletico Madrid ace is even more dangerous when agitated.
"He is an old-fashioned type of centre-forward because he seems to like to get motivated on the physical aspect of it and the niggle aspect of it," Allardyce was quoted as saying by the Mirror.
"I have told them not to get involved in that. I think it winds him up and makes him better which is a silly thing to do."
Despite their poor form, West Ham have generally performed quite well in East London this season and have recorded victories over both Liverpool and Manchester City.
The head-to-head record over the past decade may swing heavily in favour of Jose Mourinho’s men, but that won’t stop the hosts from giving it a real go and trying to lift the mood around a subdued Upton Park.