Musharraf removed the judges, widely thought to be critical of his rule, last November.
The ruling coalition, which came to power in elections in February, has vowed to restore the judges, but disputes have put the government under strain.
Lawyers gathered outside Chaudhry's house in Islamabad on Saturday, applauding as he emerged to leave for Peshawar.
"We have strong belief that we will success because this is a genuine demand and without free and independent judiciary Pakistan cannot survive," Baz Muhammad Kakar, president of Baluchistan bar council, said.
Beleaguered president
The restoration of the judges would be seen as a blow to Musharraf, who has already faced calls for his resignation from members of the ruling coalition.
But the president has been able to count on support from outside Pakistan.
George Bush, the US president, telephoned Musharraf on Friday, expressing support for the increasingly beleaguered Pakistani president and Pakistan's ties with the US.
Musharraf has been a key ally in Bush's so-called "war on terror".
Sadiqul Farooq, a spokesman for the party of Nawaz Sharif, a former prime minister whose party is now the second-largest in the ruling coalition, criticised Bush for his support of Musharraf.
Farooq said Bush should have told Musharraf to quit and that his party did not regard the call as friendly or pro-democratic.