Complex Event Processing (CEP) is an emerging field with important applications in many areas. CEP systems collect events arriving from input data streams and use them to infer more complex events according to predefined patterns. The Non-deterministic Finite Automaton (NFA) is one of the most popular mechanisms on which such systems are based. During the event detection process, NFAs incrementally extend previously observed partial matches until a full match for the query is found. As a result, each arriving event needs to be processed to determine whether a new partial match is to be initiated or an existing one extended. This method may be highly inefficient when many of the events do not result in output matches. We present a lazy evaluation mechanism that defers processing of frequent event types and stores them internally upon arrival. Events are then matched in ascending order of frequency, thus minimizing potentially redundant computations. We introduce a Lazy Chain NFA, which utilizes the above principle, and does not depend on the underlying pattern structure. An algorithm for constructing a Lazy Chain NFA for common pattern types is presented, including conjunction, negation and iteration. Finally, we experimentally evaluate our mechanism on real-world stock trading data. The results demonstrate a performance gain of two orders of magnitude over traditional NFA-based approaches, with significantly reduced memory resource requirements.