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Atletico, through to the last four of Europe's elite club competition for the first time in 40 years, dominated the defence-minded 2012 winners but were unable to carve out an advantage ahead of next week's return leg at Stamford Bridge.
Chelsea coach Jose Mourinho, returning to the Spanish capital after three years at Atletico's city rivals Real, had clearly set out to frustrate the home team and the result means his side will be slight favourites to advance to next month's final in Lisbon.
The Londoners lost goalkeeper Petr Cech when he fell heavily and hurt his right elbow in the 15th minute but neither his replacement Mark Schwarzer nor Atletico keeper Thibaut Courtois were genuinely tested in a drab affair.
There was another cracking atmosphere before kickoff at the 55,000-capacity stadium next to the Manzanares river where the fans have been flocking to enjoy what is easily the Madrid club's best season in almost 20 years.
Atletico coach Diego Simeone deployed an attacking formation with Diego Costa leading the line supported by attacking midfielder Raul Garcia and Diego and Koke providing the creative impetus just behind.
Mourinho, by contrast, had containment in mind, with former Atletico captain Fernando Torres alone up front and defender David Luiz in a holding role in a five-man midfield.
The Portuguese coach had obviously instructed his players to sit back and try to catch Atletico on the break and they were happy to let the home side have the ball in a first half short on entertainment.
Chelsea were forced to make an early change when Cech was knocked to the ground by a tumbling Raul Garcia at a corner and he was helped off clutching his right arm.
Australian Schwarzer, 41, making only his second Champions League appearance, became the oldest player to feature in the knockout phase.
With almost the entire Chelsea team behind the ball, the hosts managed only one shot on target before the break, a weak Diego effort, and the visitors none.
Midfielder Mario Suarez flashed a long-range drive narrowly wide in the 34th minute and Diego Costa had a volley well blocked by Cesar Azpilicueta but otherwise there was little goalmouth action.
The second half was a similarly cagey affair and there was more bad news for Chelsea in the 73rd minute when captain John Terry limped off after turning his ankle at a corner.
Captain Gabi forced a decent save from Schwarzer in the 76th minute as Atletico pressed for a goal but Chelsea held out reasonably comfortably.
