According to Wikipedia:
Burma-Shave was introduced in 1925 by the Burma-Vita company, owned by Clinton Odell. The company's original product was a liniment made of ingredients described as coming "from the Malay Peninsula and Burma." Demand was sparse, and the company sought to expand sales by introducing a product with wider appeal.
The result was the famous Burma-Shave advertising sign program, and sales took off. At its peak, Burma-Shave was the second-highest selling brushless shaving cream in the United States. Sales declined in the 1950s, and in 1963 the company was sold to Phillip Morris. The signs were removed at that time. The brand decreased in visibility and eventually became the property of the American Safety Razor Company.
In 1997, the American Safety Razor Company reintroduced the Burma-Shave brand, including a nostalgic shaving soap and brush kit. In fact, the original Burma-Shave was a brushless shaving cream, and Burma-Shave's own roadside signs frequently ridiculed "Grandpa's old-fashioned shaving brush."