I am a citizen of Zambia and currently work for a software company in the U.S. under Optional Practical Training (and have been working for 8 months). I want to work on a 7 month project in Canada and would like to apply for a work permit. Would I have to receive an offer letter from the Canadian company and have the position approved by HRSDC or would there be another way to apply for a permit?

The requirements of the case will depend on a number of factors, including the details of the work to be done and the details of your qualifications. If your case does not fall under any exemption from a Labour Market Opinion, then the offer would have to be first favourably reviewed by Service Canada (HRSDC) prior to eligibility for a work permit.