Four others were killed and at least 50 people were hurt in the attack.
Mr Chatah, a Sunni Muslim, was an adviser to ex-PM Saad Hariri. He was also a staunch critic of Syrian President Bashar al-Assad and Lebanon's Shia Hezbollah movement that backs him.
There has been a wave of attacks in Lebanon, linked to heightened Sunni-Shia tensions over the Syrian war.
Saad Hariri implicitly accused Hezbollah of carrying out the attack.
He blamed "those who are hiding from international justice and who have spread the regional fire to the [Lebanese] nation".
Five Hezbollah suspects are due to go on trial in three weeks' time, charged in connection with assassinating Saad Hariri's father and former Prime Minister, Rafik, in a huge car bombing in February 2005.
Hezbollah has denied involvement in Rafik Hariri's death.
