In 2006, three Middlesbrough fans were stabbed while in April 2007, 11 Manchester United supporters ended up in hospital due to incidents before their semi-final first leg.
Last December, seven United supporters were taken to hospital after the two sides met again in the group stages, although their quarter final in April passed by without incident.
The Champions League Final is being staged in Rome this season, but Uefa's president Michel Platini has already warned that it could be taken away from their stadium if there is any more serious violence involving Roma's fans.
The Blues will arrive in Rome in buoyant mood after Saturday's 5-0 thrashing of Sunderland at Stamford Bridge.
Nicolas Anelka fired a hat-trick and hailed Chelsea manager Luiz Felipe Scolari for helping him put the fire back into his game.
Anelka said: "The manager said he wanted to see more fire from me this season.
"He has put me on the pitch and it's working.
"The more you play, the stronger your game becomes and you can be confident."
