The summoney sidequest is located in Flora, which is the city you go to in chapter 2. Just talk to the people with blue blips on them to activate the sidequest. Theres two, one for each of the Ranger and Summoner.
It's definitely chapter two. You can get the Summoner class prior to encountering the second owl. It is obtained to the west of Florem from one of the three Venus sisters. Killing all of them nets you Summoner, Ranger and Valkyrie. All of these are done before getting Red Mage.