The Eminem Show, featuring the single Without Me, sold about 285,000 copies for the week ending on Sunday, the first day it was officially made available for sale.
This appears to have been due to unofficial early sales. The album was reportedly sold in some US shops from Friday, after the record company Universal let retailers have the CD for Sunday sales.
Eminem's last album The Marshall Mathers LP sold 1.7 million copies in its first week of release in 2000.
But the rapper has also been a favourite with computer users, something that will concern rather than please his record company bosses.
US music database service Gracenote had Eminem at number two in its Digital Top 10 before the album was officially released.
The vast majority of the tens of thousands of users listening to The Eminem Show must have been using pirate copies, analysts contend.
The chart recognises the CDs being played in individual computers using special software that connects to mainstream players such as Winamp and Windows Media Player.
First time
Players check a database when a new CD is put into a computer, allowing the software to tell a listener the name of the CD and its song titles.
"It's pretty safe to say that it's all CD-Rs that people have bought off the streets or burned from friends," said Gracenote chief executive David Hyman.
"This is the first time anything unreleased has shown up at number two."
Gracenote's charts does not include "soft" formats such as mp3 or other such downloads.
Eminem is currently number one on the Digital Top 10.
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