Should United have won or lost, it would have constituted a club record of 19 games without registering a draw.
This was a point that the hosts richly deserved against an in-form side who would have gone third with victory and have turned their season around under Thomas Tuchel.
Leeds’ record of not beating a side in the top-half of the Premier League table at home may have extended, but this was a rewarding afternoon and a positive step in the right direction.
Leeds gave as good as they got and could have nicked victory in a second half where they posted threat in front of the Kop. A shame it was empty and that home supporters could not suck in a famous winner.
There was plenty to admire about United, with the likes of Tyler Roberts, the wonderfully consistent Raphinha, Diego Llorente and Illan Meslier all having good afternoons, in particular.
The one downer was the sight of top-scorer Patrick Bamford hobbling off in the first half on a day when captain Liam Cooper did not feature. It was due to sickness, Marcelo Bielsa revealed afterwards.
No goals may have arrived in the first half, but it still proved a compelling watch and a very presentable spectacle for supporters watching across the globe in a match-up of two of the world’s great coaching brains.
The crossbar shuddered at each end, albeit in contrasting circumstances.
The bad news for Leeds was the sight of a player so fundamentally important to their cause and at the heart of everything good in their play this season in Bamford making way with injury in the 35th minute after landing heavily following an aerial challenge with Antonio Rudiger.
It offered Rodrigo a rare chance to showcase his wares up top and down the middle, briefly.
Leeds’ best first-half moment arrived when Roberts - earlier denied by an offside flag when he converted from Bamford’s pass - see his goalbound effort tipped onto the woodwork in outstanding fashion by Edouard Mendy on 15 minutes.
Four minutes before that, a comedy moment almost saw Chelsea take the lead when a clearance from Luke Ayling cannoned off Llorente and hit the bar, with Meslier a helpless bystander.
Chelsea had the better of it and posted particular danger down their right with Christian Pulisic, but Leeds were tactically disciplined without the ball and in no way overawed against an in-form visiting side who were unbeaten in 11 matches under Tuchel.
With Timo Werner not involved, the onus at the business end was on Kai Havertz, who failed to convert a good early chance after an excellent cross from Pulisic and fired at Meslier after a clever pass from Hakim Ziyech moments before the interval.
Straight after, he was denied by a strong tip-over by Meslier, although you got the impression that Werner may have been a bit more clinical if he was around - and not cooling his heels on the bench.
Mendy then excelled himself again to produce a fine one-handed save to keep out Raphinha’s attempt from close in after Rodrigo nodded down a Roberts’ centre - on an afternoon when both goalkeepers were convincing in their work.
All the while, you wondered how long Tuchel would leave it before potentially introducing Werner or Olivier Giroud - and there were other possible game-breakers too in an embarrassment of riches.
Leeds survived another scare when Chilwell was put off at the last second by Jack Harrison before steering his effort wide after he ghosted in on the overlap.
Chelsea may have had the better of it, but the hosts certainly had their moments, with only an important intervention from Pulisic preventing Raphinha from getting a clear shot at goal at close-blank range in front of the deserted Kop.
At the other end, Meslier’s commanding afternoon continued when he kept out Rudiger’s effort, while Leeds continued to persevere in their quest for a famous win.
They continued to knock on the door with good work by Roberts and Raphinha teeing up Llorente, who almost crowned a good afternoon with a goal, with his goalbound shot deflected just over by Reece James before Rodrigo headed the resultant corner from Raphinha straight at Mendy - before being substituted for Klich and suffering the misfortune to be replaced after earlier coming on himself.
No winner transpired but this was an excellent point for Leeds, make no mistake.
Leeds United: Meslier; Ayling, Llorente, Stuijk, Alioski; Phillips; Raphinha, Roberts, Dallas, Harrison (Costa 64); Bamford (Rodrigo 35 (Klich 79). Substitutes unused: Casilla, Koch, Poveda, Berardi, Shackleton, Jenkins.
Chelsea: Mendy; Azpilicueta, Christensen, Rudiger, Chilwell; Kante, Jorginho; Pulisic (James 68), Ziyech (Werner 69), Mount (Hudson-Odoi 79); Havertz. Substitutes unused: Arrizabalaga, Alonso, Zouma, Kovacic, Giroud, Emerson Palmieri.