Quite where it comes from, though, is an open question. Military men used it to refer to the stripes on the arm of one's uniform, so that to chance one arm meant to take a calculated risk, which might end in a court martial and demotion.

What does chancing their arm mean?

[British] to do something risky or adventurous in order to get something you want. Instead of going on the dole I chanced my arm on a business. Easy Learning Idioms Dictionary.

Where is the door of reconciliation?

Dublin's most fascinating door hangs inside Saint Patrick's Cathedral. It no longer serves its' original purpose. What is known today as the Door of Reconciliation, hangs within the sanctuary of this famous church, in a gallery exhibit for historic artifacts?