We present a simple random model for food web connectance. We model observed webs as random samples drawn from the universe of all possible randomly connected sets of n objects, with no biological interactions assumed. We then drop out links based on observed link-magnitude data and sampling effects. The resulting connectance curves nicely bracket real data, suggesting (1) that food webs may in fact be randomly connected, and (2) the mere fact that previously proposed models can generate the observed connectance values does not guarantee the correctness of the models. This study also suggests that studies of food web topological properties may bear reexamination.