This fare is available for travel starting as soon as next week, departures are valid for Monday, Wednesday, Friday, and Saturday travel through the end of September. Returns in October are available. You'll have to flexible with dates to find this fare but if you search on the AA site you should be able to piece an itinerary together at this price.
As an example, I found seats departing ORD on Saturday, September 1 and returning on Wednesday, September 5, 2018.
This fare books into American's basic economy fare, meaning flights before September 5, 2018, your carry-on allowance to just one small personal item such as a purse or small backpack up to 18x14x8 inches. Other restrictions apply. Consider the higher regular economy fare if you require more carry-on allowance.
Need a room in Phoenix? Here's what's available for the listed dates on Hotelwatchdog.