Short Answer: Yes (In batches of 20)
The American supermarket chain has sold USPS stamps from their locations for a number of years. They offer a great location to pickup some postage stamps while you are doing your usual shopping routine. It is worth noting that you are only able to be a sheet of stamps (20 stamps) and that individual stamps are not available. The price of the sheet of stamps is sold at the same price as you would find at a USPS store or kiosk. Many stores are open from 8am to 10pm or even later so if you have a hectic schedule they can be a great place to buy stamps outside of regular business hours.
While there you will also be able to by envelopes, pens, paper etc so if you need to send a letter and don't have any supplies they will likely be able to sort you out with everything you need. Many of their large stores also feature USPS mailing services allowing you to attach a postage stamp and send the letter right away. Since the year 2000 Safeway has also began delivering groceries. This means you can have your groceries delivered to your door and with them a sheet of stamps.
If you are away from home and would like to find a Safeway store near you then the maps below should be a great help. All you need to do is enter your city or postcode into the box and if there are any stores nearby they should show up on the map.
Safeway is on of the countries largest retail/grocery store chains with over 1300 locations scattered throughout the United States. They even have a number of international stores which can be found in Canada, Mexico, England, Australia, and Germany. The success of Safeway and its expansion throughout the United States and internationally is a testament to the businesses management as well as their 250'000+ employees. Safeway also runs a number of subsidary companies you may have heard of including Carrs-Safeway, Pak n' Save, Pavilions, Randall's, Tom Thumb, and Von's which are all likely to offer postage stamps if you are looking for them.
In researching postage stamps from Safeway we stumbled accross a New York Times article from 1988 which mentioned a promotion that Safeway was running. A bold coupon strategy had the stores selling $4.40 worth of stamps for $4 (cheaper than you could buy them from the Post Office). As far as we can tell this was the first know example of a large scale store selling stamps at below value. The fact that it made the NY Times shows how rare this would have been. As to when they first started selling stamps we could not find out, it could have been just about any time since the business began in 1915 and sadly these things are often not recorded.