Is it part of the Status bar, or part of the lower frame of the browser? If I recall Firefox 3.6 correctly, you can toggle the display of the Status bar using:

View > Toolbars > Status Bar

Some add-ons can cause the "gray bar" problem. You could try disabling all non-essential extensions under Tools > Add-ons, restart Firefox, and see whether that helps.

Help pages related to add-ons:

Troubleshooting extensions and themes | Troubleshooting | Firefox Help
Troubleshooting plugins | Troubleshooting | Firefox Help

Article on the mozillaZine site (different site): Gray bar below status bar - MozillaZine Knowledge Base

Sounds that you have an extension or theme that has changed the appearance of the Status bar.

Start Firefox in Diagnose Firefox issues using Troubleshoot Mode to check if one of the extensions or if hardware acceleration is causing the problem (switch to the DEFAULT theme: Firefox/Tools > Add-ons > Appearance/Themes).

• Don't make any changes on the Safe mode start window.
• https://support.mozilla.org/kb/Safe+Mode

• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

Thank you to both jscher2000 and cor-el! The page Jscher linked really helped; turns out the Trend Micro toolbar was causing the 'gray bar'. Thanks so much!