Via the Southwest Facebook account:

Southwest Airlines For 72-hours only! We’re celebrating 39 years with $39 one-way fares! (taxes, fees, and exclusions apply). Read all the details and book your tickets here:

You can get all the details and book here.

Here are a few more details:

For 72 Hours Only, We’re Gonna Party Like It’s Our Birthday!
No need to bring a present to this birthday bash; we’re giving you one instead! For the next three days, you can score some of our most amazingly awesome deals of the year for travel September 8 – November 17, 2010. Our gift to you!

Don’t miss out on this limited-time-only party favor. Book by June 24, and let the celebration live on through your next vacation!