The jury of eight women and four men was sworn in at Preston Crown Court to hear historical allegations that Hall, 84, raped and indecently assaulted two young girls.
He is charged with seven counts of rape against one complainant between 1976 and 1978. Five of the rapes are said to have taken place when she was under the age of 16.
Hall is also accused of two counts of indecent assault against the woman within the same period.
In addition, he is charged with eight counts of rape and three indecent assaults against a second alleged victim between 1976 and 1981.
One of those alleged rapes is said to have taken place when the complainant was aged under 13.
Last year, Hall, from Wilmslow, Cheshire, pleaded guilty to 14 offences of indecent assault against 13 girls or young women at the same court and was jailed for 15 months. The sentence was subsequently increased to 30 months by the Court of Appeal.
Prosecutor Peter Wright QC said: "You see the defendant seated in the dock. You may recognise him as a former radio and TV personality, and broadcaster of many years."
Hall, wearing a dark suit, white shirt and striped tie, listened on from the dock as he wore a large pair of headphones.
The former It's A Knockout presenter has pleaded not guilty to all 20 allegations.
He earlier pleaded guilty to one count of indecent assault between 1978 and 1979 against a girl aged under 16.
He has been a familiar face and voice in British broadcasting for half a century, and his eccentric and erudite football match summaries made him a cult figure.