Antonio’s Conte’s men made if four straight wins without conceding by beating Southampton 2-0 on Sunday to move within a point of the top of the table.
Luiz is out to take the Premier League trophy back from Leicester following the Blues’ pitiful defence of their crown last season.
And the Brazil defender, while admitting he expects the title race to be the most tightly contested for years, insisted: “We are title challengers.
“It will be like this until the end. It is still just the beginning and the end is more important than the beginning.”
Luiz, who returned to Chelsea in the summer after winning two league titles with Paris St-Germain, hailed the effect that Conte is having on the troops after last season’s disastrous showing which cost Jose Mourinho his job.
He said: “Mr. Conte works hard with us and tries to give a lot of information for us to prepare the plans for the games in the best way.
“Diego Costa, Eden Hazard, Pedro, Willian or Oscar, it doesn’t matter who is playing”
Chelsea defender David Luiz
“It is important to continue this way. If you sleep for one minute you start to lose and then you lose one, two, three matches. We have to be awake all the time.
“We need to keep our feet on the floor. We try our best ever match and try to improve our level. We know the Premier League isn’t easy.
“We know when you start the game nobody knows who will win. We keep working hard and we are doing great.
“We try to improve our level every single match, we train hard every day.”
Chelsea have not conceded since Conte switched to a 3-4-3 formation and Luiz reckons striker Diego Costa should take some of the plaudits for their new-found solidity.
Luiz said: “It is everybody, not just the three at the back, that are not conceding goals.
“The first defender is Diego. The mentality of the team when we don’t have the ball is good.
“It is great everybody only speaks about the three defenders or the goalkeeper, but it is not like that.
“Diego, Hazard, Pedro, Willian or Oscar, it doesn’t matter who is playing. They are doing great in the side which makes it much easier for us.”