If you are a single member LLC and you did not choose to be taxed as a corporation, the IRS will treat the LLC as a "disregarded entity" for tax purposes. You would then file a schedule-C or C-EZ to report the income and expenses of the business. In this case, if you have no income and no expenses from the business, you would not be required to report anything on schedule-C.
If, however, it is a multi-member LLC or you plan to have your single member LLC be taxed as a partnership or a corporation, then you should file a return for the LLC even if there is no income and no expenses.
The choice on how to report to the IRS is made on your first tax return filed for the LLC and this remains as the method of reporting for the life of the LLC. It can be changed in subsequent years only if you get IRS agreement with the change.