Subdomains and WordPress Installations

Hello WordPress Forum!

We are trying to figure out how to create a website that will be a directory of services and there will be a city-specific page for various cities around the country (much like Craigslist for those in the USA).

We would have the home page at “ourwebsite.com” and then subdomains for each city like so: “chicago.ourwebsite.com” and “seattle.ourwebsite.com” , etc etc –

MY QUESTION:
To create something like this – – would we have to have a separate installation of WordPress in EACH subdomain, along with a separate installation of the WP theme? (wow!)

Hope my post makes sense – thank you!