The CBI had sought to set aside a special judge's March 5 order that directed the agency to allow inspection of documents kept in the 'malkhana'.
The high court had on May 18 stayed trial proceedings in the case involving Chidambaram and his son Karti.
It also sought that the ED rectify the discrepancies in the page numbering of the record and also supply missing documents.
A bench headed by Justice R Banumathi set aside the Delhi High Court's September 30 verdict denying him bail in the corruption case.
CBI had registered a case regarding irregularities in granting FIPB clearances to INX Media in 2007 when P Chidambaram was finance minister.
The Congress leader, who was also the home minister during UPA 2, was sent to judicial custody for 14 days in a corruption case related to the INX Media group.
The span will cover Chidambaram's 74th birthday - on September 16 - which he will have to spend locked up.
The apex court, while denying anticipatory bail to P Chidambaram in the INX Media case, said it must be left to the discretion of the investigating agency to decide the course of the probe.
Both lawyers agreed and told the bench that they will not press for interim bail before the trial court till the apex court passes the order.
When it comes to the question of liberty, the courts do not go into technicality, a bench of Justices A K Sikri and Ashok Bhushan said.
The CBI today moved the Supreme Court challenging a Delhi High Court order granting bail to Karti Chidambaram, son of senior Congress leader P Chidambaram, in the INX Media case.
After coming out of CBI headquarters here, Chidambaram said he had appeared before the CBI and the FIR did not contain any allegations against him.
Chidambaram's alleged role came under the scanner of investigating agencies in connection with the Foreign Investment Promotion Board (FIPB) clearance of Rs 305 crore.
The Delhi High Court had yesterday granted Chidambaram interim protection from arrest till July 3 in the case.
Justice A.K. Pathak directed the Central Bureau of Investigation (CBI) not to take any coercive action against Chidambaram till July 3, the next date of hearing.