Do I have to file a 'zero' Tax Return with the IRS?

yes, if you have an LLC you probably already have to file quarterly or as per your state's regulations. Regardless of the frequency even if you are making zero sales, zero expenses, etc. you need to report them as the files are due.

Yes, you definitely have a U.S. tax filing obligation. A single member LLC is a disregarded entity for U.S. federal income tax purposes. Although the entity itself does not pay federal income taxes, the single owner is responsible for reporting the income and expense of the LLC on his/her income tax return and paying the requisite income tax, if applicable. If the LLC does not generate any U.S. source income, and you do not conduct business in the U.S. through a permanent establishment, then the LLC probably does not owe any U.S. federal income taxes. However, the IRS has recently implemented new regulations which require single member LLC's to file a Form 5472 to report the activity of the LLC. This form is filed alongside a proforma Form 1120. It is absolutely critical that you file these returns. The IRS can impose a $25,000 USD penalty for noncompliance. I highly recommend you consult a competent U.S. tax adviser that specializes in these filings.

You never have to file.

And if you don't the IRS may assign a tax bill to your company via random number generation or whatever crazy valuation they're using at the time for your type of business.

Best for very person (SS number) + every entity (EIN) should file a tax return, even if $0 tax is required.

If the IRS assigns a tax value, you will spend countless hours trying to straighten this out.

Also, if you have an entity which is fallow (no longer used), shut it down, so you can avoid undo paper work filings every year.