Yes you do need a visa - the only way it can be waived is if you booked and pay for an organised tour before you enter the country - then the tour operator can apply for waiver - but it is not guaranteed.
You may be able to obtain the visa at your point of entry.
Check with
http://www.zambiaembassy.org/
2419 Massachusetts Avenue, NW
Washington DC 20008
Telephone: (202) 265-9717