The absolute deadline for eating chametz is the morning before Passover.
It is forbidden to eat chametz until the close of the festival in eight days.
Since the commandment to rid one's domain of chametz is binding only on a Jew, you can sell your chametz to a non-Jew, and then buy it back from him after Passover . The area where the chametz is held is leased to the non-Jew for the duration of the festival. This sale is not symbolic but a 100% legally binding transaction, and must therefore be conducted by a competent rabbi.
The morning of Pesach, you take the bag with chametz from last night's search, plus any other leftover chametz that you're not going to sell, make a fire, and burn it.
