We consider covert communication using a queuing timing channel in the presence of a warden. The covert message is encoded using the inter-arrival times of the packets, and the legitimate receiver and the warden observe the inter-departure times of the packets from their respective queues. The transmitter and the legitimate receiver also share a secret key to facilitate covert communication. We propose achievable schemes that obtain non-zero covert rate for both exponential and general queues when a sufficiently high rate secret key is available. This is in contrast to other channel models such as the Gaussian channel or the discrete memoryless channel where only $\mathcal{O}(\sqrt{n})$ covert bits can be sent over $n$ channel uses, yielding a zero covert rate.