Consider n sensors whose positions are represented by n uniform, independent and identically distributed random variables assuming values in the open unit interval (0,1). A natural way to guarantee connectivity in the resulting sensor network is to assign to each sensor as range the maximum of the two possible distances to its two neighbors. The interference at a given sensor is defined as the number of sensors that have this sensor within their range. In this paper we prove that the expected maximum interference is Ω(ln ln n), and that for any ∈ > 0, it is O((ln n)1/2+∈).