A thrilling 2-2 Premier League draw at the Emirates Stadium a week ago was followed by a cagey encounter here.
The Blues had the better opportunities to take a first-leg lead, but Cesc Fabregas and Andreas Christensen spurned headed opportunities either side of half-time in a 0-0 draw.
Fabregas wanted a penalty after a Danny Welbeck challenge in the 88th minute, but play continued when referee Martin Atkinson consulted Video Assistant Referee Neil Swarbrick and it was determined Welbeck got the ball.
The second leg takes place on January 24 at the Emirates Stadium, when a place in the Wembley final, against Manchester City or Bristol City, will be at stake.
Should Chelsea advance, it would alter the scheduled February 25 Premier League duel with Jose Mourinho’s Manchester United at Old Trafford.
Antonio Conte and Arsene Wenger have a mutual dislike of Mourinho, whose United side won the League Cup last season.
The competition represents the Gunners’ best chance of silverware, given their FA Cup defence is already over.
Wenger experienced defeat in the third round for the first time in his 21 years in charge at Nottingham Forest last Sunday.
Alex Iwobi started at Chelsea despite facing a fine for partying ahead of the Forest loss. Alexis Sanchez was only a substitute as speculation over his future continues.
Chelsea reverted to a near first-choice line-up, although captain Gary Cahill was omitted altogether.
Wenger was serving the second game of a three-match touchline ban by sitting in the press box.
The contest was less pulsating than a week ago, but it might have been different had Alexandre Lacazette been more composed early on. Instead the striker blasted off target after breaching the offside trap.
Victor Moses tested David Ospina, twice cutting in from the right to fire left-footed at the Gunners goalkeeper.
The VAR was available for the second time in English football.
Atkinson consulted Swarbrick first after Calum Chambers pushed over Cesar Azpilicueta as the pair jostled for position at a corner. Both received a ticking off.
Then Atkinson spoke into his head set after Iwobi’s shot was parried by Thibaut Courtois and Ainsley Maitland-Niles beat Moses to the ball in the Chelsea box. The Arsenal wing-back hurdled his Chelsea counterpart, but there was no contact.
Some unsavoury tackles may have merited further scrutiny. Hector Bellerin caught Fabregas late and seconds later Chambers fouled Eden Hazard from behind.
Chelsea rued two missed headed chances either side of half-time.
Azpilicueta’s lofted pass was met by Fabregas six yards out. But the Spain playmaker headed straight at Ospina.
Christensen, having inadvertently blocked a N’Golo Kante shot, then headed over from close range at the far post.
There were muted Chelsea appeals for handball by Shkodran Mustafi in blocking a Danny Drinkwater shot.
Next Alvaro Morata went close. Ospina saved a 25-yard shot from the striker, who then found the outside of the post from the most acute of angles.
Mustafi blocked a Moses shot and Christensen headed wide from the resulting corner.
Iwobi ran at Chelsea on a rare Arsenal attack after 72 minutes which culminated in a toe-poke which Courtois gathered.
Chelsea were pressing to break the stalemate, but half-chances came and went.
Fabregas fell in the box after pursuing a ball with Welbeck, who appeared to get the ball.
Atkinson again consulted Swarbrick, with play continuing.