Border Security and Immigration Enforcement Act of 2017 This bill amends the Immigration and Nationality Act to replace the diversity visa program with a paying immigrant program under which an immigrant visa can be obtained by paying a $1 million fee (and a $500,000 fee for an accompanying child under the age of 18). The bill establishes a fiscal year limit of 55,000 visas for such immigrants. A Border Security and Immigration Enforcement Account is established in the Treasury for such fees (except for certain of such fees allocated to individuals who facilitate the application process for such immigrants) which shall be used for U.S. Immigration and Customs Enforcement and U.S. Customs and Border Protection. Such an immigrant who otherwise meets the naturalization requirements shall be naturalized within two years (rather than five years) of being lawfully admitted for permanent residence.