I would like to have a project for Chicago area. I will need small (low end) VPS.
lowendbox suggests me removed
Actually I do not need 2GB RAM, but I like their pricing (no more then $10).
So is anyone from Chicago and can suggest better deal?
Or the one is the best?

Have you tried searching google for reviews of the company lowendbox suggested to you? Keep in mind that they are a business so most likely the company that they recommended pays for that suggestion but they still may be worth a look at if they meet your requirements

What company is meant here?

I wouldn't limit the search to just Chicago. You should look at Toronto, NYC, and etc. There are a lot more options that can fit your needs better.

vpswebserver.com Based in Chicago.It is specialized in providing Microsoft Hyper-V VPS hosting,network and OS administration experts with at least 10 years of experience in the IT field.

On the server side, vpswebserver uses two highly regarded data centers located in Chicago and Philadelphia which come with the highest amount of interconnectivity, redundancy and security imaginable plus they have 24/7/365 on-site data center technicians to ensure complete reliability. More specifically, VpsWebServer’s spacious Chicago facility, which is also the home to many of its managed dedicated server and Virtual Private Server clients, has allowed the company to effectively and competitively scale its prices.

hey try cloudclaim they are the best, I am with them since long. You can check out their plans for vps hosting, cloud hosting, etc they provide fair discounts too and satisfactory

Also, what type of platform are you looking to get?
Linux or Windows?

From your budget, I would assume you will want Linux since Windows licensing costs are pretty high.