Klebnikov, the editor of Forbes magazine's Russian edition, was gunned down in the Russian capital in July 2004.
Two of the defendants are charged with carrying out the killing. The third, a Moscow notary, is accused of organizing the criminal group that carried out the murder.
Prosecutors say that Klebnikov was killed on the orders of another Chechen, Khozh-Akhmed Nukhaev. Nukhaev, who remains at large, was the subject of a critical book written by Klebnikov.
A defense lawyer, Ruslan Khasanov, said all three defendants pleaded innocent at the court hearing.
The U.S.-based Committee to Protect Journalists on 9 January criticized the court's decision to close the jury trial to the public and called for a "transparent and credible prosecution."
Klebnikov had investigated murky business dealings and corruption in post-Soviet Russia.