Thomas Mair, 52, has been charged with Cox's murder. Asked by the judge what his name was, he repeated several times "My name is death for traitors, freedom for Britain."
"Yes," said Chilton, asked whether the killing happened suspiciously timely for those who support the Remain campaign.
"What happened was on Thursday, just a week before the referendum," Chilton continued.
He, however, did not want to speculate on who could be behind the murder in this context.
"There is no good timing for anything like this, it's a tragedy. Now we are in the situation where people are respecting the memory," he said.
Chilton stressed also that the murder would change the mood of the debate, with people expected to treat the vote more respectfully.
Voters across the United Kingdom will take part in a referendum on Thursday to decide whether or not the country should exit the European Union.
