The mosquitoes were found in Pittsburg, and the chicken was from Oakley.
So far in the county this year, four people, 87 dead birds, 31 groups of mosquitoes, nine squirrels, 15 chickens and three horses have tested positive for the virus, the district said.
District officials are urging residents to remove standing water around their homes and to report abandoned or neglected swimming pools, which are a major source of mosquitoes in the county.
The district will conduct fogging in areas of Pittsburg at dusk tomorrow.
To report a mosquito problem, call the Contra Costa Mosquito and Vector Control District at (925) 771-6195. For information about West Nile virus symptoms, prevention or testing, call Contra Costa Health Services at (888) 959-9911.