Territorial Tax Parity Act of 2017 This bill amends the Internal Revenue Code to modify the income source rules involving U.S. possessions, including Guam, American Samoa, the Northern Mariana Islands, Puerto Rico, and the Virgin Islands. Under current law, income is not considered to be possession source income if it is treated as income: (1) from sources within the United States, or (2) effectively connected with the conduct of a trade or business within the United States. The bill amends this rule to specify that it applies to the extent that the income is attributable to an office or fixed place of business within the United States. The bill also revises the source rules for personal property sales. The Internal Revenue Service may limit the application in the Virgin Islands of requirements for U.S. citizens and resident aliens to pay a tax to a foreign country to be considered a nonresident of the United States for certain personal property sales.