Adding to Jon's correct answer, please refer to the "ASA New Features by Release" document.
Specifically, Table 46 which shows:
Table 46 New Features for ASA and PIX Version 8.0(2)/ASDM Version 6.0(2)
The ASA supports EIGRP or EIGRP stub routing.
In case you're wondering, 8.0(2) was released in June 2007.
Hardware support for the 5500-X series was introduced as of 8.6 software in 2012. It included all of the EIGRP features from before and has been further enhanced moving forward into the current 9.x releases.