We analyze the population of periodic variable stars in the open cluster NGC 3766 based on a 7-year multiband monitoring campaign conducted on the 1.2 m Swiss Euler telescope at La Silla, Chili. The data reduction, light curve cleaning, and period search procedures, combined with the long observation time line, allowed us to detect variability amplitudes down to the millimagnitude (mmag) level. The variability properties were complemented with the positions in the color-magnitude and color-color diagrams to classify periodic variable stars into distinct variability types. We encourage searching for this new class of variables in other young open clusters, especially in those hosting a rich population of Be stars.