From the first page of the December 6, 1990 Maeil Gyeongje:
"LG 25 is Born!
Now you can purchase all the things you need in life 24 hours a day."
According to the ad, the first store opened near Kyunghee University in Seoul.
As I mentioned here, the first convenience store in Korea was a 7-Eleven, which opened in May 1989. LG 25 has been GS 25 for five or six years now.
One thing I've noticed is that many stores come and go, but convenience stores tend to stay (though they may change franchise names). In Banghwa-dong I can only think of one (a Family Mart) that closed, but that was likely because there was a Buy the Way 15 meters away, and a 7-11 about 40 meters away.