When does community assembly lead to a predictable species composition and when does this process depend on chance events, such as the timing of species arrivals? We studied the combined effects of enrichment and predation on the occurrence of priority effects, i.e. dependency on the timing of arrival, using a model of a small food web consisting of a predator, two competing prey and interference through allelopathy. Our analysis shows the conditions under which priority effects can occur. In the system we studied, the interfering species has to be the weaker resource exploiter of the two consumers, or it has to be more susceptible to predation. When it is the weaker resource exploiter, a minimum level of nutrient input is required for interference to be strong enough to cause a priority effect. When the interfering species is more susceptible to predation, a priority effect actually requires predation, which in itself also requires a minimum level of nutrient inflow. However, the priority effect disappears when predation pressure rises above a threshold value, also when the two competitors are equally preferred by the predator. This is so because predation reduces population densities and thereby the strength of interference. Our analyses make clear how the effects of resources and predation can combine to result in the absence or presence of priority effects during community assembly.