This paper investigates the capacity of a channel in which information is conveyed by the timing of consecutive packets passing through a queue with independent and identically distributed service times. Such timing channels are commonly studied under the assumption of a work-conserving queue. In contrast, this paper studies the case of a bufferless queue that drops arriving packets while a packet is in service. Under this bufferless model, the paper provides upper bounds on the capacity of timing channels and establishes achievable rates for the case of bufferless M/M/1 and M/G/1 queues. In particular, it is shown that a bufferless M/M/1 queue at worst suffers less than 10% reduction in capacity when compared to an M/M/1 work-conserving queue.