Well, the Nicolet Watch Co. of Tramelan is a well-known manufacturer, with chronographs apparently being their main product. Usually they were equipped with Landeron movements- notably the column wheel calibres 13 and 39 (and their derivatives). Your watch has what appears to be a Valjoux 72C:
bidfun-db Archive: Watch Movements: Valjoux 72C
What seems odd, is that everything seems to match except the hairspring stud carrier, but that changed over the entire period of production- for example, the hairspring stud carrier in your watch is the same as in the version of Valjoux 72 made for Rolex under the name Rolex 72. So yeah, IMO it's positively a Valjoux 72C.

I don't think that there's any way of telling what year exactly was this watch made- the Valjoux 72C was in production 1946-1974, as stated in the Ranfft archive. Style-wise, I think it's from the 1950s, given that it has a shock device- mid to late 1950s. Frankly, I wonder why did you say "1920-1940"? The looks of this watch, and the fact that it has a shock device (hardly any chronographs had that until the 1950s), pretty much rule the interwar period out.

 

Hello, Nice chrono. Check out the Valjoux 88.

 

lovely watch !
yes, it clearly is a Valjoux R88; would assume 1950s

 

Nine columns in the columns wheel generally mean Valjoux. I think that one of the calendar wheels (day-of-the-week or month) must be a replacement since the two don't match in colour.....

Hartmut Richter