I used to live in San Jose (GO SPARTANS) and all of my neighbors had chickens (We lived off of Snell Rd near Santa Teresa)
They kept very small flocks of 2-3 tops but seriously everyone had them and the cutest of cute coops for them. My neighbor Glenda had a pink coop that was relatively small but she let her girls wander her back yard when she was home in the evenings and in the mornings.
I think you might approach them with a plan. How you will care for them, how often you will clean after them (weekly) Then bring in the benefits of chicken poop composted into the soil for plants. Also have a plan for the initial start up and where you will raise the chicks or if you are getting grown girls. (heat lamps, pine litter, feed) Don't get a rooster. My girls did eat every green thing in their run so keep that in mind too.
A couple of chickens are not stinky if you keep their houses clean. Daily water changes - benefits that they will eat the left overs of foods and be like little garbage disposals and produce eggs. Growing up, we were part of the Mission 4-H club. I did not have chickens but all my friends did.
At the time, my Mom would not go for it but now that I am all grown up with my own kids, I have chickens, my mom thinks they are great.
Good luck
Caroline