A Hero's Tale Edit
You must complete the puppet show on fable2.com and choose one of the crowns at the end. If you play through it 3 times you can get all of the stuff by choosing a different crown each time. You must have Xbox Live and must not open the chest until you've played through the show enough times to get all you want.
See: A Hero's Tale
Originally, you had to complete the puppet show at fable2.com, but the service has since been discontinued. A temporary alternative site now has a message which confirms the final closure of the service: Unfortunately, after almost four years it was time for us to close down the Fable II chest in the Chamber of Fate. Have fun in Albion! For full details, please see A Hero's Tale.
Fable II Limited Edition Edit
There were also some things included with the Fable II Limited Edition that were found in the chest as well. Such as Hal's Armour and Hal's Sword. If you do have the limited edition it can opened as soon as you reach the Guild, meaning you have a reasonable weapon to start with.