In Mrs Capel’s will, the chain was left to her son – but it is not known how it came to her possession.
Documentary makers said it was a royal chain of office, which would have been irreplaceable, and forever linked with its owner, as well as being priceless.
They added Sir James’ alleged involvement in the disappearance of the princes was first reported by Sir Thomas More, who claimed he had hired two men to carry out the killing.
Prof Thornton said: “The identification of the chain is significant as powerful men of that time wore collars or chains made out of precious metals as expressions of their identities.
“These chains would have carried symbols or badges of their associations and loyalties and of who they were, so this is a very personal possession of the King, clearly identified as his and it is in the hands of Margaret Capel.”