Can I claim the Foreign Housing Exclusion but NOT Foreign Income Exclusion? I contributed to a Roth IRA so I can't exclude my foreign income, as it's my only income.

Thank you for your patience and for this question.  After some research, I did find that this is allowed.   My apologies for the incorrect initial answer.  

TurboTax does not have a way to do this our online software or in the interview mode of the program, but you can do this via an override on the form itself.   

To do this using the desktop software (CD or download version), enter all of your information as if you are going to exclude all of the income using the Foreign Earned Income Exclusion and the Housing Exclusion.  

Then switch to the Forms mode by clicking on the Forms icon in the upper right of the program.

Find Form 2555, p. 3 in the list of forms on the left.  Right-click on Line 42 to override the amount of the Foreign Earned Income Exclusion and type 0.  This will still transfer the housing exclusion to Line 8 of Schedule 1 as a negative income adjustment.  

Overrides in the software do disqualify the return from electronic filing, so you will need to print this return and mail it in for processing. 

However, this will allow you to have the earned income needed to permit your Roth IRA contribution and does appear to be permitted according to both the form instructions and IRS Publication 54.

So, yes, you can simply fill in the Housing Exclusion section of Form 2555 and take only that exclusion on your tax return and report your income on your tax return. 

Thank you again for this question and for allowing me some time to get the right answer to you.