The probability distribution of a single stock is studied by analyzing a database (the Trades and Quotes Database) documenting every trade for all the securities listed in three major US stock markets, for the two year period Jan 1994 - Dec 1995. A sample of 40 million data points are extracted which is substantially larger than studied hitherto. A power law asymptotic behavior is observed, with an exponent alpha approximately 3 for the cumulative distribution, which is well outside the Levy regime (0 <alpha < 2).