Yes, under certain circumstances.
The Vacaville Municipal Code permits home chicken keeping as a non-commercial accessory use to single family residences in zones with a 6,000 square foot or larger minimum lot size (Agricultural (AG), Hillside Agriculture (AH), Rural Residential (RR), Rural Estate (RE), and the Residential Low Density RL-10, and RL-8, RL-6 zones). It allows keeping of up to one adult hen chicken per 1,000 square feet of lot area, up to a maximum of 9 hens. Roosters are not be allowed. See Vacaville Municipal Code - Home Animal Keeping. If you have a question about which zone you are in, see the online Zoning Map.
The height of coops and runs is limited no more than six feet plus one foot for every foot setback from a property line.
The Community Development Director is allowed to make certain exceptions to accommodate a disability, a 4-H or similar type project, or other exceptional circumstances. See the Special Animal Keeping Permit.
All premises where animals are kept must be kept in a clean and sanitary condition and that fowl cannot escape onto neighboring properties. See Vacaville Municipal Code - Animal and Fowl Regulation and Vacaville Municipal Code - Animal Nuisances.
If you have a complaint about chickens, visit the Code Enforcement page about how to file a complaint.