They are four away from Arsenal's all-time record of 14 but, with Crystal Palace, Bournemouth and Stoke on the fixture list before the end of 2016, Antonio Conte's side may harbour hopes of beginning the new year with history at stake against Tottenham.
Here, Press Association Sport's Tom White looks at the Premier League's longest winning runs.
14 WINS
ARSENAL, February-August 2002
Arsene Wenger's side finished their 2001-02 title-winning campaign with 13 successive wins and then beat Birmingham 2-0 in the opening game of the next, before a 2-2 draw with West Ham ended the run
It is the longest ever winning run in the English top flight, equalled in the second division by Manchester United in 1904-05, Bristol City the following season and Preston in 1950-51.
12 WINS
MANCHESTER UNITED, March-August 2000
United won the 1999-2000 title by a thumping 18-point margin, rounding it off with 11 straight wins and scoring 37 goals in the process - the run included 4-0 wins over Bradford and Sunderland, a 4-3 success at Middlesbrough and a 7-1 dismissal of West Ham featuring a Paul Scholes hat-trick
They opened the following season with a 2-0 win over Newcastle before drawing 1-1 against Ipswich.
11 WINS
CHELSEA, April-September 2009
Guus Hiddink's first spell as the Blues' interim manager ended - in league terms at least - with successive wins over West Ham, Fulham, Arsenal, Blackburn and Sunderland
Carlo Ancelotti then opened up with six straight wins to establish the club record Conte's men are threatening, before the run was surprisingly ended by Wigan with the help of a Petr Cech dismissal and goals from Titus Bramble and Paul Scharner
Regardless, Chelsea went on to win the league and FA Cup double.
MANCHESTER UNITED, December 2008-March 2009
Following United's return from the Club World Cup and against the backdrop of the famous press conference at which Rafael Benitez, then manager of title rivals Liverpool, read out his list of "facts", the Red Devils won 11 in a row
Liverpool themselves ended the run by winning 4-1 at Old Trafford but Sir Alex Ferguson's men finished four points ahead of their rivals to claim a third straight title.
LIVERPOOL, February-April 2014
Liverpool's title challenge was powered by the club's longest winning run in the Premier League, which itself brought 38 goals for a free-flowing side fronted by Luis Suarez
It was memorably ended by defeat to Chelsea after Steven Gerrard's unfortunate slip before, having been 3-0 up with 11 minutes to play, they capitulated to draw with Crystal Palace.
MANCHESTER CITY, April-September 2015
City finished as Premier League runners-up to Chelsea despite winning their final six games of the 2014-15 campaign
They opened last season with five more, before West Ham put a stop to their run, and failed to challenge surprise champions Leicester
Source : PA
Source: PA