A no-chamber was a construct that hid whatever was inside it from prescient/oracular vision. It also appeared to render the contents invisible and undetectable in other ways.
Some evidence suggests that the first no-chamber was invented by a scientist named Chobyn prior to the ascent of Paul Atreides. According to these sources Chobyn created the no-chamber for the Baron Vladimir Harkonnen. Millenia later, it was in this no-chamber that Duncan Idaho and Miles Teg hid during their escape from the Bene Tleilax on Gammu.
This technology was lost, and then re-invented by the Ixians. The first of these new no-chambers was constructed on Ix. Inside this chamber Hwi Noree was grown by the Ixians with biological technology they bought from the Bene Tleilax. The development of the chamber itself was a combination of efforts on other devices such as a device that recorded the thoughts of Leto II into a written journal, a device that hid the journals from prescient vision, and experiments that created a navigation machine that replaced a Spacing Guild Navigator.
Another of the new no-chambers was used at Dar-es-Balat, where the journals of the God Emperor were hidden.
The no-chamber technology was later incorporated into the no-ship.
Behind the Scenes
The exact origin of the no-chamber is not given by Frank Herbert. The storyline crediting Chobyn as the first creator of the no-chamber is made by Brian Herbert and Kevin J. Anderson.