Accelerating Holding Foreign Companies Accountable Act This bill revises provisions related to the required certification to the Securities and Exchange Commission by certain publicly traded companies that they are not owned or controlled by a foreign government. Under current law, a company must make this certification if the Public Company Accounting Oversight Board is unable to audit specified reports because the company has retained a foreign public accounting firm not subject to inspection by the board due to a position taken by an authority in that foreign jurisdiction. Under this bill, a company must submit this certification if a position taken by any foreign government (not only the foreign government in which the firm is located) prevents inspection of the firm. Furthermore, under current law, if the board is unable to inspect the company's public accounting firm for three consecutive years, the company's securities are banned from trade on a national exchange or through other methods. The bill reduces this time to two consecutive years.