Questionable refereeing, last gasp equalizers and penalty heartache have all conspired to dump the Blues out at the semi-final stage of Europe's premier competition four times since 2004.
They went closest to claiming the top prize in the 2008 final but were denied when John Terry famously slipped with the chance to seal victory in a sudden death shoot-out against Manchester United.
High time: Cech thinks Chelsea deserve to be crowned champions of Europe
However, under the guidance of new manager Carlo Ancelotti, himself a four-time Champions League winner as a player and a manager with AC Milan, Chelsea are have rediscovered the ruthlessness that led them to back-to-back domestic titles.
Now they want, and according to Cech deserve, to taste European success.
'We hope every year that it's finally going to be the year that we win the trophy because over the years we've deserved so many times to get our hands on it,' the stopper said. 'We hope that this year's going to be the year.'
Dejected: The Blues have came closest to winning the Champions League in 2008 but lost on penalties to Manchester United
On Wednesday Chelsea became only the second English team to win at Porto's Est?o do Drag? securing progress to this season's knockout stage as Group D winners. The 1-0 victory, courtesy of Nicolas Anelka's sixth goal this season, was the seventh clean-sheet in the Londoner's last eight matches.
Largely responsible for that impressive run are Cech and defender Ricardo Carvalho. After the match in Portugal, the former Porto defender hailed the impact of manager Ancelotti.
'He's added something to our team,' the Portuguese explained. 'But we have to bear in mind that he inherited a very strong group of players. He likes the tactical aspects of the game and we have tactical sessions almost every day in training and that allows us to correct any mistakes we're making.'
FC Porto 0 Chelsea 1: Anelka adds a gloss finish to a dull nightHiddink tug of war: Bayern set to thwart Chelsea by swapping Van Gaal for GuusVilla tells Chelsea, United and Man City he will consider £35m Valencia exitALL CHELSEA FC