The company is believed to be converting its Giraffe site in the Cabot Circus shopping centre to the fried chicken brand for a 29 November opening.
Slim Chickens was founded in Fayetteville, Arkansas in 2003 and has expanded to over 80 US locations.
BRG has held the franchise rights in the UK since 2018.
It has opened locations in London, Cardiff and Birmingham, with several sites replacing BRG’s existing Giraffe and Ed’s Easy Diner restaurants.
“We have had a fantastic response to our brand and our chicken in the locations we have opened so far and we hope to create more 'Slimthusiasts' with the amazing people of Bristol with our new restaurant," says Tom Crowley, CEO at BRG.
BRG says it has “ambitious growth plans” for the brand, with more restaurants planned to open in key cities across the UK in 2020.