Territorial Tax Parity Act of 2019 This bill modifies the income source rules that apply with respect to the taxation of income from U.S. possessions (Guam, American Samoa, the Northern Mariana Islands, Puerto Rico, and the Virgin Islands). Under current law, income is not possession source income if it is treated as (1) income from sources within the United States, or (2) as effectively connected with the conduct of a trade or business within the United States. The bill amends this rule to specify that it applies only to the extent that the income is attributable to an office or fixed place of business within the United States. The bill also modifies the income source rules that apply to certain personal property sales in the Virgin Islands.