You can totally own chickens in the city. There's not really an acreage requirement but technically you have to have them 15 feet from neighboring dwellings which could be a challenge in some lots. The city puts out a whole guide to chickens in Richmond: https://www.rva.gov/sites/default/files/2019-04/RACCChickenGuide.pdf

You do need a license. $60/year I believe. Up to 6 birds. No roosters