I have a dim recollection of having heard that when humans gain weight, adipose cells just get larger, rather than dividing. True?
My foray into the literature suggests that mature adipocytes do not divide. See, for example:
Lefterova, MI et al. (2009) New developments in adipogenesis. Trends in Endocrinology and Metabolism 20:107-114
In the context of looking at the possibility of stimulating the conversion of white adipose tissue to brown adipose tissue, the authors outline the way in which the expansion of adipose tissue occurs by a process in which fibroblast-like pre-adipocytes differentiate into cells capable of storing lipid droplets and responding to insulin.
It appears therefore that expansion of adipose tissue occurs by the generation of new adipocytes. Thinking of the morphology of a fully-loaded adipocyte (a lipid droplet surrounded by a narrow band of cytoplasm) it seems rather unlikely that these cells would be capable of division. The Wikipedia citation linked to by QuietThud in the comments to the OP is to a popular book on nutrition, not an authoritative source.