If I remember correctly, we budgeted a certain amount each semester in a philanthropy category to cover advertising, supplies, etc. If we decided to take on an extra philanthropy, we would vote to spend the money on it (and could recoup our money from the proceeds as long as we didn't advertise that EVERYTHING would be donated to the cause. Want to avoid false advertising here! And let me add that we never kept a lion's share of the proceeds. It all depended on what we were doing and how it all worked out).
I'm not sure exactly what kind of fundraiser you have planned, but if your chapter couldn't cover the startup costs, what about partnering with another group. Would the American Cancer Society help out with advertising? What about businesses donating their services in exchange for acknowledgement of their donation? Check out the resources that are in your area.
Hope this helps!!