(1) Condit had an affair with former staffer Joleen Argentini-McKay, which ended in 1996.
(2) When it ended McKay gave him the man's Tag Heuer watch as a gift.
(3) Chandra Levy was seen regularly wearing the same type of watch (man's, Tag Heuer) by her coworkers at the Bureau of Prisons. This is 5 years later, 2001.
(4) Tag Heuer watchcases have a serial number matching the watch. When Condit dumped the watchcase, hidden inside a McDonald's container, in the trash in an Alexandria, Virginia park, because of the serial number the watchcase was traced back to McKay, who originally bought the watch as a gift for Condit.
My opinion/conclusion is Condit probably gave Chandra the watch his ex-lover Joleen Argentini-McKay gave him years earlier, and by ditching the watchcase, which in a roundabout way could be traced back to him via McKay, he was trying to erase the Chandra connection since she always wore the watch -- otherwise there would be no reason to dump the watchcase.