I believe that ZICH (ЗиЧ in cycrillic) was a brand of bicycles produced in Novosibirsk by Aviation Factory no 153. This factory was named after Valery Chkalov, an iconic Russian test pilot and Soviet hero of the 1930s. You sometimes see the bikes referred to using the word Chkalov (Чкалова), and it is possible that ZICH is actually initials for something like ‘Zavod imeni Chkalov’ (‘Завод имени Чкалова’ or ‘Factory named after Chkalov’). Please excuse my total lack of Russian, but hopefully you get the idea.
The seminal bicycle model was the ZICH-1, a three speed derailleur touring bike that was revered in the Soviet Union for its quality, finish and capability. It appeared in 1946 and was possibly only produced until 1948. Despite this short production run, and in the tradition of living fast and dying young, it appears to have held a surprising grip on the affections of a generation of Russian cyclists. Think of it as the Jimi or Janis of post-war Soviet cycling.
The ZICH-1 used a derailleur that was a clear copy of a Simplex bell crank operated touring model, such as a Grand Prix or Grand Touring.