We introduce an RF nanoreceiver, based on a forest of carbon nanotube (CNT) antennas packaged together. Based on the physical model of a charged carbon nanotube under RF exposure, which is significantly different from a typical RF antenna, we analyze the performance of our nanoreceiver. We show that, for low signalbandwidth applications, our nanoreceiver is highly robust, allowing for continual operation over extended periods of time at low probabilities of error at reasonably low SNR values. For high signal-bandwidth applications, we show that at a given SNR, the achieved rate grows as n1/4 with the number, n, of the CNTs, at reasonably low probabilities of error. Due to the extremely small scale of the CNTs, many millions of CNTs can be packed into very small areas (e.g., hundreds of millions in 1 mm2) to achieve rates comparable to the commercially available wireless receivers. Hence, significant spatial miniaturization is achieved by our nanoreceiver compared to a classical RF receiver without a loss in the achievable rates.