Intel® Core™2 Duo Processor E4300 - Is it a 64 Bit Processor?

"Yes, all Core 2 Duo chips are 64-bit capable, that is includes the EM64T feature. Of course, if your running a 32-bit OS then it'll be no different then a 32-bit chip, but if you
put a 64-bit OS on your system the Core 2 Duo chips will handle
it properly. So yes it is capable of running 64-bit Windows.

however please note;

Intel® EM64T requires a computer
system with a processor, chipset,
BIOS, operating system, device drivers
and applications enabled for Intel
EM64T. Processor will not operate
(including 32-bit operation) without
an Intel EM64T-enabled BIOS.
Performance will vary depending on
your hardware and software
configurations.

http://processorfinder.intel.com/details.aspx?sSpec=SL9TB"

All Intel Core-2 processors contain the 64 bit instuction sets.