We develop an approach to solve curriculum-based course timetabling (CB-CTT) problems with Large Neighborhood Prioritized Search (LNPS) based on Answer Set Programming (ASP). LNPS is a metaheuristic that starts with an initial solution and then iteratively tries to obtain improved solutions by alternately destroying and prioritized searching for a current solution. Our approach relies on high-level domain-specific LNPS configurations for efficient CB-CTT solving, and both the grounding and solving tasks are delegated to a heuristically-driven answer set optimizer implementing the LNPS algorithm. The resulting system teaspoon-lnps demonstrates that LNPS can significantly enhance the solving performance of ASP for CB-CTT solving. Furthermore, we show the competitiveness of our declarative approach by empirically contrasting it to the best known bounds obtained by more dedicated algorithms.