A closed electromagnetic resonant chamber (RC) is a highly favorable artificial environment for wireless communication. A pair of antennas within the chamber constitutes a two-port network described by an impedance matrix. We analyze communication between the two antennas when the RC has perfectly conducting walls and the impedance matrix is imaginary-valued. The transmit antenna is driven by a current source, and the receive antenna is connected to a load resistor whose voltage is measured by an infinite-impedance amplifier. There are a countably infinite number of poles in the channel, associated with resonance in the RC, which migrate towards the real frequency axis as the load resistance increases. There are two sources of receiver noise: the Johnson noise of the load resistor, and the internal amplifier noise. An application of Shannon theory yields the capacity of the link, subject to bandwidth and power constraints on the transmit current. For a constant transmit power, capacity increases without bound as the load resistance increases. Surprisingly, the capacity-attaining allocation of transmit power versus frequency avoids placing power close to the resonant frequencies.

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