The big-spending Londoners won the title in 2005 and 2006 under former coach Jose Mourinho but since then have been runners-up twice and third last season.
Avram Grant, Luiz Felipe Scolari and Guus Hiddink have all failed to emulate Mourinho's double triumph and this time the task of toppling United from top spot falls to former AC Milan supremo Carlo Ancelotti.
"It will be close, as it has been for the last four or five years," defender Terry told the club's website as his team prepared for Saturday's home league game with Hull City.
"We have been pushing them (United) closely and when we won it, they were pushing us, so it will be a fight to the death.
"I am sure at the same time Liverpool, Arsenal and Manchester City will be pushing and upsetting a few good teams as well," added England skipper Terry who last month turned down a money-spinning move to City.
Chelsea ended their pre-season campaign in encouraging style, beating United 4-1 on penalties when the traditional Community Shield curtain-raiser at Wembley ended 2-2 after 90 minutes.
One of the chief talking points of that game was Chelsea's new 4-4-2 playing style preferred by Ancelotti.
Mourinho's title-winning teams adopted a 4-3-3 strategy and that system was retained by successors Grant, Scolari and Hiddink.
Since Nicolas Anelka joined Chelsea in January 2008 it has been rare to find him and fellow striker Didier Drogba paired together in the same starting lineup.
MIDFIELD DIAMOND
Ancelotti, though, seems keen to employ both goalgetters ahead of a four-man midfield diamond formation.
"He (Ancelotti) wants us to be organised, win the ball back as quickly as we can and play good, attacking football," said vice-captain Frank Lampard.
"The manager has settled very quickly and we have picked up his ideas very quickly so the improvements will come.
"He is very easy to work for in terms of his man management," added the England midfielder. "He is a very nice man and a very strong man on the training ground so everyone has reacted to that and now we're looking forward to going into the season."
Chief among the reasons for Ancelotti's recruitment by billionaire Russian owner Roman Abramovich were his two Champions League triumphs with Milan.
Winning Europe's elite club competition for the first time may be Abramovich's top target this season but Lampard left no one in any doubt about his own priority.
"For me it is the Premier League," said the former West Ham United player. "I grew up watching the Premiership and the league before that and it's a lovely feeling to be the best team in your country and I want to get that back.
"The Champions League is definitely something I want to win at least once in my career but for me the Premier League is where we need to get to the consistency levels we had a few years ago."
