The New York Court of Appeals — the highest court in New York state — says no.
The case is People v. Weaver (PDF), released today:
GPS is not a mere enhancement of human sensory capacity, it facilitates a new technological perception of the world in which the situation of any object may be followed and exhaustively recorded over, in most cases, a practically unlimited period. The potential for a similar capture of information or "seeing" by law enforcement would require, at a minimum, millions of additional police officers and cameras on every street lamp....The court bases its decision solely on the New York constitution, so there can be no recourse to the U.S. Supreme Court. This is the law in New York: "in the absence of exigent circumstances, the installation and use of a GPS device to monitor an individual's whereabouts requires a warrant supported by probable cause."
The whole of a person's progress through the world, into both public and private spatial spheres, can be charted and recorded over lengthy periods possibly limited only by the need to change the transmitting unit's batteries. Disclosed in the data retrieved from the transmitting unit, nearly instantaneously with the press of a button on the highly portable receiving unit, will be trips the indisputably private nature of which takes little imagination to conjure: trips to the psychiatrist, the plastic surgeon, the abortion clinic, the AIDS treatment center, the strip club, the criminal defense attorney, the by-the-hour motel, the union meeting, the mosque, synagogue or church, the gay bar and on and on. What the technology yields and records with breathtaking quality and quantity, is a highly detailed profile, not simply of where we go, but by easy inference, of our associations -- political, religious, amicable and amorous, to name only a few -- and of the pattern of our professional and avocational pursuits.