Support for Chaudhry has grown into a broad campaign for the restoration of democracy and is seen as a significant threat to Musharraf who came to power in a coup in 1999.
For nearly a month the supreme court has been listening to legal arguments aimed at determining which judicial body should rule on the misconduct charges against Chaudhry.
"It would be in the best interests of Pakistan for Musharraf to step down"
Jim ibarra, Cyberjaya, Malaysia
Send us your views
Chaudhry had challenged the impartiality of a panel set up to conduct the inquiry, and its hearings were halted pending the outcome of the supreme court's deliberations.
Now the court has brushed aside a government attempt to block Chaudhry's challenge saying it will consider the case.
Aitzaz Ahsan, the lead counsel on Chaudhry's legal team, said: "We are very happy and satisfied that the court has begun regular proceedings."
A government lawyer rejected the notion that it was a setback.
Ahmed Raza Kasuri, a lawyer for the government, said: "Nothing has been said against the government. There is nothing adverse."
The government appears determined to get rid of Chaudhry and had said on Sunday that another misconduct complaint had been prepared against him.
Analysts believe that Musharraf's motive for seeking to dismiss Chaudhry stemmed from doubts he would be supportive in the event of constitutional challenges to the president's election plan.
Musharraf has said he will seek re-election by the sitting national and provincial assemblies before they are dissolved for a general election around the end of the year.
He is also believed to be reluctant to give up his post of army chief, as he is constitutionally required to do by the end of the year.
According to a statement filed in the supreme court last week, the accusations against Chaudhry include falsifying expenses, harassing judges, bias in appointments and intimidating police and civil servants. Chaudhry has denied wrongdoing and has refused to resign.
Ahsan says the new complaint against Chaudhry shows the government's lack of confidence in its initial accusation.
"If the government files a new reference, it means they have lost confidence in this one and their main purpose is not rule of law but the ouster of chief justice," he said.
Chaudhry has made several trips out of Islamabad to meet supporters among the legal fraternity over recent weeks.
An attempt to address a rally of lawyers in Karachi on May 12 sparked the worst political violence in Pakistan in years.
About 40 people were killed when pro-government activists clashed with opposition supporters hoping to welcome Chaudhry to the city. There has been no violence since then.