Erin,
The default stacking order for an object with fill and stroke, such as a simple path, is that the stroke is on top and the fill is beneath it.
You may change that in the Appearance palette, but it should not be necessary.
Can you show a screenshot with the object and the Appearance palette and the Layers palette with the relevant (part of the) Layer expanded and visible?
If things are really wrong, you may start considering going down this dark road:
The following is a general list of things you may try when the issue is not in a specific file (you may have tried/done some of them already); 1) and 2) are the easy ones for temporary strangenesses, and 3) and 4) are specifically aimed at possibly corrupt preferences); 5) is a list in itself, and 6) is the last resort.
1) Close down Illy and open again;
2) Restart the computer (you may do that up to 3 times);
3) Close down Illy and press Ctrl+Alt+Shift/Cmd+Option+Shift during startup (easy but irreversible);
4) Move the folder (follow the link with that name) with Illy closed (more tedious but also more thorough and reversible);
5) Look through and try out the relevant among the Other options (follow the link with that name, Item 7) is a list of usual suspects among other applications that may disturb and confuse Illy, Item 15) applies to CC, CS6, and maybe CS5);
Even more seriously, you may:
6) Uninstall, run the Cleaner Tool (if you have CS3/CS4/CS5/CS6/CC), and reinstall.