The squeeks are in the subfloor...if you have an open ceiling basement, there are several methods to eliminate the squeeks.
Here is a site that gives 7 different ways to silence squeaky hardwood floors:
You can try dusting the floor with talcum powder and sweeping it into joints. Longer lasting repairs can be effected by utilizing Squeeks No More screws and adapter with your drill. The screws are designed to beak off below floor level, adhering into floor joists. You can then fill any indentations with saw dust and wood filler, before sanding and staining, if desired.
You must measure out from doorways to calculate location of joists, if you lack access from beneath, in which case you need only screw through joists into flooring.
You can see the Squeeks No More in action on This Old House website, with Tom Silva.
Chalk probably does the same thing as talcum powder. Never tried it but read about it.
Olivia is spot on! Baby powder works great