* Benazir Bhutto's son makes makes first major address
* Too young at 24 to contest 2013 election
* Hundreds of thousands attend rally outside mother's tomb
LARKANA, Pakistan, Dec 27 (Reuters) - The only son of assassinated former Pakistani prime minister Benazir Bhutto told hundreds of thousands of supporters on Thursday, the fifth anniversary of his mother's death, that he would carry forward her legacy, an appearance designed to anoint him as a political heir.
"I am the heir to the martyr," Bilawal Bhutto Zardari, 24, told the crowd in the southern province of Sindh, referring to his mother and to his grandfather, the founder of the current ruling party who was hanged by a former military ruler.
"If you kill one Bhutto, there will be a Bhutto in every house."
Bhutto was joined by hundreds of high-ranking officials, including the current president, his father Asif Zardari, to commemorate his mother's killing in a gun and suicide attack during a 2007 political campaign rally.
Making his first address to a mass rally televised live, he said: "Bhutto is not a name, it is an obsession, a passion, a love. You can chain our feet to the ground but we will still keep moving."
Prime Minister Raja Pervez Ashraf told followers waving the Pakistan People's Party's green, black and red flag that the Oxford-educated Bhutto "will prove to be an important turning point for democracy and politics".
Bhutto was named party chairman after his mother's death, but his father was named co-chair due to his youth.
He is still not old enough to contest the elections scheduled for spring - the minimum age is 25. Bhutto, who has his mother's good looks, will only turn 25 in September.
Zardari, locking arms with his son and waving to the crowd, said: "Bilawal has completed his studies, but the time has now come to complete his political training, to stay in Pakistan among its people and learn from them."
Benazir Bhutto's killer has never been caught and a U.N. inquiry found that Pakistani authorities had failed to protect her or properly investigate her death. The U.N. also said that high-ranking Pakistani officials had tried to block its investigation.
In a 30-minute address delivered alongside his mother's onion-domed tomb, Bhutto denounced the courts for what he said was the slow pace of the trial of her alleged killers. He also touched on women's rights, insurgent violence, and the economy.
Benazir Bhutto has become a powerful symbol for the ruling party, which often refers to her as a martyr. The capital's airport and a scheme to give cash to poor families have been named after her. Officials hang her portraits on walls.
The Bhuttos championed the rights of the poor in a country where feudal landlords owned vast tracts of land and agricultural workers often live in deep poverty. Many rally participants waved portraits of Benazir Bhutto wearing her trademark white headscarf.
Her husband, elected following her death, is less popular. Zardari was jailed on corruption charges from 1996 to 2004 that he says were politically motivated.
The president is locked in a power struggle with the Supreme Court, which has been battling to reopen corruption cases against him. Zardari's aides say he has immunity.
Many Pakistanis are angry that Zardari's government has failed to tackle pervasive corruption or end the daily power cuts that have brought its industrial sector to its knees.
The elections should mark the first time in Pakistan's history that one elected civilian government hands power to another.
The nuclear-armed country of 180 million people has a history of military coups. After one such coup, the new military ruler hanged Benazir Bhutto's father in prison in 1979.
Benazir Bhutto served civilian governments as prime minister twice but was dismissed on corruption charges both times.