The first part of this paper is devoted to a new CCD investigation of stars in the field of the LMC cluster NGC 1866. Two main frames have been analyzed, one covering the cluster's central region and the other covering an area about 10' from the cluster's center, and data has been collected for 2207 objects. On this basis, a C-M diagram has been derived, which shows a well-developed blue sequence reaching a limiting magnitude of about V=21mag together with the already known sequence of the cluster's He-burning giants. A new feature in our data is represented by the evidence for a second group of less luminous giants clumping around V=19mag, which we interpret as field He-burning giants. The second part of the paper is devoted to a comparison of these data with theoretical calculations. On the basis of new evolutionary tracks we find that the composition Y=0.28, Z=0.02 already used by Becker and Mathews (1983ApJ...270..155B) offers an adequate fitting of the observed range in color spanned by cluster He giants. Theoretical isochrones for this composition have been produced and are compared with the observed distribution of cluster stars. A good agreement with the observed C-M diagram is achieved for a cluster age of the order of t=100Myr, whereas field stars appear to be significantly older, with ages of about 500 Myr or more. The distribution of cluster stars is studied, and both the luminosity function of the blue sequence (BS) and number of He giants relative to BS stars are examined. We find that both these cluster characteristics can be reproduced with a Salpeter slope for the initial mass function, overcoming previous difficulties raised by suggestions of a serious disagreement between theory and observations in this cluster. The Appendix reports data for the evolutionary models and for the corresponding isochrones, covering both the H- and He-burning phases