Carlo Ancelotti's side, who host struggling West Ham on Saturday, are the Premier League's form team after winning five and drawing one of their last six matches.
That run has catapulted them back into the title race just in time for the season finale.
In contrast, leaders United - who entertain Everton on Saturday - dropped two points in a 0-0 draw at Newcastle on Tuesday, crashed out of the FA Cup against Manchester City and also have a Champions League semi-final first-leg against Schalke next week.
Arsenal, who travel to Bolton on Sunday, have fared even worse in recent weeks, with five draws from their last six matches leaving them in third place.
United remain favourites to win the sprint to the finish line, but Cech is convinced second placed Chelsea are capable of catching Sir Alex Ferguson's men.
"They have to play a Champions League semi-final, so let's see how they cope," Cech said.
"We have one competition to focus on which, is to our advantage because we can prepare all week and get more rest.
"We've been saying for a long time we want to keep winning and maintain the pressure on everybody.
"Arsenal are third for the first time in a long time so let's see how they cope with this new situation. They had plenty of chances to close the gap and haven't taken them.
"United have to play us and Arsenal so there could possibly be six points dropped by them.
"We have two games at home against West Ham and Spurs to come and, if we win both, the situation could change again."
While Chelsea have been revitalised by their winning run, Arsenal are a team low on belief after blowing leads against Liverpool and Tottenham.
A penalty deep into injury-time rescued a point for Liverpool last Sunday and then Tottenham came from 3-1 down to draw 3-3 in Wednesday's north London derby.
Those were significant blows to an already fragile group and Arsenal winger Andrei Arshavin admits the title could be beyond them now.
"We are fighting, but we have few chances," Arshavin said. "To catch up with Manchester United is of course very difficult.
"The main task for us now is to achieve maximum points from our remaining matches."
The battle for fourth place promises to be just as enthralling, with Manchester City currently clinging onto the last Champions League spot ahead of Tottenham.
Although FA Cup finalists City could be passed by Tottenham by the time they face Blackburn on Monday, boss Roberto Mancini is relaxed about his team's top-four challenge.
"Everything is in our hands," Mancini said. "We do not depend on Tottenham or other teams. If we win our games we will go in the Champions League."
Spurs striker Peter Crouch concedes his team must beat West Bromwich Albion at White Hart Lane on Saturday to stay in the hunt, but the England international claims all the pressure is on City.
"They're under more pressure than we are," Crouch said. "That doesn't make us have any less desire to get in there but we have probably got a bit more freedom than them."
At the other end of the table, third bottom Blackpool will be boosted by the news that captain Charlie Adam is fit to face Newcastle after suffering a foot injury in last weekend's defeat against Wigan.
Bottom of the table Wolves host Fulham, while fourth bottom Wigan face a massive clash against Sunderland, who are five points from the relegation zone and look in freefall after losing eight of their last nine matches.
Assistant coach Gary McAllister will take charge of Aston Villa for their home game against Stoke as manager Gerard Houllier rests in hospital after being taken ill earlier in the week.
Fixtures (1400GMT unless stated):
Saturday
Aston Villa v Stoke, Blackpool v Newcastle, Chelsea v West Ham (1630GMT), Liverpool v Birmingham, Man Utd v Everton (1145GMT), Sunderland v Wigan, Tottenham v West Brom, Wolves v Fulham
Sunday
Bolton v Arsenal (1500GMT)
Monday
Blackburn v Man City (1900GMT)
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