Use the Delete Anchor points button on the properties bar after selecting the points on these lines with the Lasso tool or by making a selection box with the Direct Selection tool
Do these two objects need to remain separate from each other? Since it looks like you were trying to line up the paths anyway, this problem can be very easily solved by merging the two objects.
You can combine the two objects by selecting both shapes and clicking on the "Unite" option in the Pathfinder panel (if you don't see the panel, go to Window > Pathfinder).
After that, you should have one shape, instead of two separate ones. You can then select the left-most anchor point using the Direct Selection tool and delete it. You should see the white area disappear.
Finally, select the two open points with the lasso tool, and join them by going to Object > Path > Join (or "control J"). You can adjust the points with the Direct selection tool to make sure the curve is nice and smooth.
Yes, would be prefer to change to one object.... I am on CS3 and I don't see unite... Is there a way to do this with CS3?
Hm...I'm not familiar with the CS3 workspace, but try this article: http://www.illustratortips.com/index.php/Instruction/Intermediate-Tips/how-to-use-the-illu strator-pathfinder-palette.html
I think the tool you should be looking for is the "Add to Shape Area" action under Shape Modes in the the Pathfinder pallette.