Barry's option #2 is probably the most common cause.
Also, it is generally not a good idea to power the MCU from the PicKit3 when there are other components connected as well (especially those that share a connection to the Vdd line). Also make sure that the MCU has all of the bypass capacitors and other required components (e.g. Vcap) connected.
Finally, make sure that there are no loads on the \MCLR\ and ICSPxx lines.
Susan