Screenshot by Matt Elliott/CNET

Amazon's Prime Now, the company's same-day-delivery offering, is now available in two more cities.

Prime Now has launched in Chicago, Illinois and Indianapolis, Indiana, Amazon announced on Thursday. The service will allow Amazon Prime members to order products and receive them in one or two hours.

Amazon launched its Prime Now rapid delivery service in December in parts of Manhattan, and has since expanded to several more cities across the US, including Dallas. Prime Now offers customers the ability to buy qualifying products -- numbering in the "tens of thousands" so far -- and have them at their doorstep within two hours. Customers who want the products delivered in one hour pay an additional $7.99.

Prime Now is available only to Amazon Prime customers who pay $99-per-year to have free two-day shipping, access to the company's Instant Video streaming service, and a library of books through the Kindle Lending Library. Prime subscribers also received a benefit on Wednesday with a special shopping day called Amazon Prime Day, offering a slew of deals on a range of products. The effort worked out for Amazon, as well: Customers around the world ordered 34.4 million items and broke Black Friday records with 398 items ordered per second.

Prime Now has proven convenient for people who want to buy last-minute gifts or, as Amazon puts it, "daily essentials," and don't want to leave home to get them. Prime Now also provides Amazon with another way to compete with local big-box retailers, including Walmart, Target, and Best Buy. Customers buying online from those companies can place an order and within minutes, run down to the store and pick it up.

Walmart, which is arguably Amazon's chief competitor, given its size, also offers same-day delivery in select cities on certain products, including groceries. Still, for now, Amazon is the top force in e-commerce in the US, but is facing increasing pressure from Walmart and other top brick-and-mortar retailers.

For years, Amazon and brick-and-mortar retailers offered two distinct business models: one promised to have products in customer homes within a few days, while the other required customers to go in-store to buy. Now, the two sides are increasingly finding themselves fighting for the same territory by offering customers simpler ways to buy online and get products to their homes within hours. Indeed, both Amazon and brick-and-mortars have a desire to make it as easy as possible for people to not have to go to a store and still have a product as soon as possible.

Prime Now is available now to customers across Chicago and Indianapolis, joining those in the Austin, Texas area, and other prominent cities. To sweeten the pot, Amazon is offering any would-be Prime Now user a 30-day free trial of Amazon Prime to try out its service.