The attack also killed five other people and threw Lebanon, which has been drawn into neighbouring Syria's conflict, into further turmoil after a series of sectarian bombings aimed at Shi'ites and Sunnis over the past year.
Former prime minister Saad al-Hariri accused Hezbollah of involvement in the killing of Mr Chatah, his 62-year-old political adviser, saying it was "a new message of terrorism". Mr Hariri added: "As far as we are concerned the suspects are those who are fleeing international justice and refusing to represent themselves before the international tribunal."
Mr Chatah's killing occurred three weeks before the long-delayed opening of a trial of five Hezbollah suspects indicted for the 2005 bombing that killed former prime minister Rafik al Hariri, Saad's father, and 21 other people.
The trial is due to open in The Hague in January. The suspects are all fugitives and Hezbollah, which denies any role in the Hariri assassination, has refused to cooperate with the court, which it says is politically motivated.
Preliminary UN investigations implicated Syrian officials.
Mr Chatah, a Sunni Muslim, was a vocal critic of Hezbollah. A message on his Twitter account less than an hour before the blast accused the group of trying to take control of the country.
The conflict in Syria has polarised Lebanon and increased sectarian tensions there.