On November 16, 1937, a subtle little ad appeared in the Los Angeles Times' lost & found column:
$2 Reward for return of each monkey escaped from Major Pictures Corp.,
1040 N. Las Palmas.
(the picture shows the address today)
It ran for five days; no idea how many monkeys were actually turned in. The New York Times, on the 19th, ran a story claiming that Belmont High School students were offered $1 a head bounty for running down monkeys that had gotten lose during the filming of a Bing Crosby picture.
A gossip-column in the Los Angeles Times reports that 150 monkeys did indeed escape from General Service Studios, which (according to seeingstars.com) is exactly what that address on Las Palmas was in 1937. Today it's Hollywood Center Studios, and seeingstars has the building's bio, from its founding in 1919, its impressive early pedigree (Howard Hughes shot Hell's Angels at this studio), and its downfall into B-moviedom, which apparently began with the escaped-monkey movie.
The movie was Doctor Rhythm, and imdb says it ostarred Beatrice Lillie, Andy Devine, and Mary Carlisle. No mention of the monkeys, but our 1937 gossip columnist claims that most of the action takes place in a zoo--hence the simians.