So far, Amazon does not allow you to delete your order/purchase history. For those concerned about privacy, however, you do have a couple options. The first is to remember that your order history is private. No one else can access your order history without access to your Amazon account. The other concern may be that your order history can affect your recommendation list, which is public. Removing order items from your recommendation list is possible.
Log in to your Amazon account.
Go to your order history.
Search through and find the items you wish to remove from your recommendation list.
Next to each item, make sure the box marked "use to make recommendations" is not checked.
Tip: If you wish to purchase a more private item, it could be helpful to open two separate accounts. This way you could use one privately and one publicly for wish lists or sharing recommendations with friends and family.