Scientific American, November 25, 1905, page 427:
This advertisement for the Electro Importing Company's new radio transmitting-and-receiving package, the "Telimco Wireless Telegraph Outfit", ("Guaranteed to work up to one mile"), first appeared in Scientific American magazine on November 25, 1905, and then began running weekly starting two weeks later. The Telimco system included a battery-operated spark transmitter, shown on the left, plus a tapping-coherer receiver, also battery operated, shown on the right. (The use of a spark transmitter and tapping-coherer receiver meant it could only be used to send and receive telegraphic dots-and-dashes, and not full audio.) This small ad--which measured just 2-1/4 inches wide by 1-1/8 inches high (60 by 28 millimeters)--appeared on the back pages of the magazine, mixed in with the advertisements for sundry offering by numerous other small firms. It is generally believed that this was the first-ever advertisement run by a company selling complete radio systems to the general public.
Hugo Gernsback later reported that some people were so suspicious whether the Telimco Outfits could really be sold so cheaply, that the New York City police department sent over an officer to check things out and make sure the ads weren't really some sort of scam. Also, at some point, Gernsback appears to have forgotten the exact date on which the first Telimco advertisement appeared. The Electro Importing catalogs from the mid-teens state that the ads premiered in Scientific American in November, 1905. However, in a special issue of Radio Craft published in March, 1938, Gernsback gave the date as January 13, 1906, and even included a picture of the January 13, 1906 ad, which is slightly different from the actual first ad that appeared six weeks earlier.
The Telimco brand name was a contraction of The Electro Importing Co. In addition to Telimco Wireless Telegraph Outfits, you could also buy Telimco Experimental X-Ray Outfits, Telimco-meters, Telimphones, etc.