There has never been an official Chief Rabbi of the United States. Jonathon D. Sarna (in his American Judaism: A History. Yale University Press, 2004, page 105) explains this phenomenon thus:
But since there was no parallel Christian religious authority—no chief Protestant minister, no archbishop, not even a Catholic cardinal with nationwide jurisdiction—it was easy for opponents to dismiss any Jewish effort to create a chief rabbinate as "ridiculous" and antithetical to American ideals. Nor, given church-state separation, could any chief rabbi expect governmental recognition, much less the kind of authority that some European chief rabbis wielded. Finally, many Americans of the day, Jews among them, were deeply suspicious of strong central authority. The "tyranny of the majority," they feared, would soon come trampling down on the rights of the minority, be they southerners or religious reformers. As a result, all efforts aimed at electing a chief rabbi ended in failure, and the decentralized congregationalist polity that characterized American Judaism since the Revolution remained in place.
There were a number of US cities that had Chief Rabbis, but the last one, Rabbi Shalom Rivkin of St Louis, MO, passed away in October of 2011 (source).