Arsenal held at Highbury
The Gunners failed to score against Manchester United last weekend - ending their 55-match Premiership goal streak - and their barren spell continued against the Spanish champions.
Freddie Ljungberg twice came close to breaking the deadlock but some inspired goalkeeping and a lack of composure in front of goal saw The Ches shut out Arsene Wenger's team.
With 20 minutes on the clock Arsenal almost went ahead with Dennis Bergkamp saw picking out an on-rushing Ljungberg in the penalty area.
The Swedish international did not know whether to head the ball or control it as it came at an awkward height. He chose the latter but his touch let him down and the chance went begging.
Talisman and skipper Patrick Vieira was then taken off and replaced by Ray Parlour on 38 minutes and Arsenal will be sweating on his fitness for crucial matches coming up.
Ljungberg produced a moment of magic in the 51st minute with a brilliant turn deceiving the Valencia defence but goalkeeper Andres Palop, deputising for the injured Santiago Canizares, was out in a flash to thwart Ljungberg's goal-bound shot.
Three minutes later Palop was on hand again to parry a Bergkamp header as Arsenal turned up the Highbury heat.
Miguel Angel Angulo then received a straight red card after 70 minutes for an elbow on Pascal Cygan and it was all hands to the pump for the visitors.
Substitutes Kanu and Sylvain Wiltord both went close late on with the latter missing a guilt-edged chance to steal the spoils.
John Carew gave Arsenal a scare at the other end with the sands of time running out but the match ended scoreless.
The result sees Arsenal stay at the Group B summit with four points from their opening two fixtures.
In the other Group B match on Tuesday night Ajax defeated Roma 2-1 at the Amsterdam ArenA.
An under-strength Ajax team - missing the likes of Cristian Chivu, Rafael van der Vaart and Tomas Galesek - made home advantage count as they joined Arsenal on four points and left Roma stranded at the bottom with nothing to show from their first two matches.
De Eredivisie champions took the lead after just 11 minutes through Zlatan Ibrahimovic following a horrific mistake from Antonioli.
The goalkeeper failed to hold a Nigel De Jong shot from distance and the Swede pounced to side-foot home.
Ibrahimovic was a thorn in the Roma rearguard throughout the encounter and only sharp defending from Walter Samuel and Jonathan Zebina denied the enigmatic striker in the second period.
But it was substitute Jari Litmanen - who has scored a number of goals in the Champions League in his distinguished career - who curled a 66th minute shot from the edge of the area to hand Ajax a 2-0 lead.
Roma threw on ageing Argentine striker Gabriel Batistuta as they searched for a lifeline.
'Batigol' produced a goal on 89 minutes to give the capital club hope but it was too little too late as Roma returned to the Eternal City pointless.
The Champions League now takes a break and resumes in February with ties taking place on 18/19th of that month.
For the match summaries click below
Ajax 2 -1 Roma
Arsenal 0 - 0 Valencia
Click here for Champions League tables