Playtex Boeing Nike Lockheed & Martin 
Answer: Playtex
When you think about the history of NASA and space exploration, you might assume that the iconic space suits of the Apollo space program were designed in house or, at minimum, by a company with a lot of experience in the aerospace industry like Lockheed & Martin.
Those sturdy space suits, in fact, were designed by none other than Playtex (then also known as the International Latex Company). While modern readers likely associate the company name with sanitary products, Playtex has a long (and continuing) history in the undergarment manufacturing business; during the latter half of the 20th century, they made bras, girdles, and other elements of the heavily structured wardrobe of mid-century American women.
Given their experience in making very sturdy and multi-layered garments as well as the skilled staff they employed to design and construct said garments, it should come as no surprise that when it came time to build a reliable space suit they won the bid. The skills required to fashion a quality girdle translated very well to precisely stitching a flexible but sturdy space-ready garment.
Image courtesy of International Latex Company/Playtex.