In this paper we demonstrate how TCP congestion control can show chaotic behavior. We demonstrate the major features of chaotic systems in TCP/IP networks with examples. These features include unpredictability, extreme sensitivity to initial conditions and odd periodicity. Previous work has shown the fractal nature of aggregate TCP/IP traffic and one explanation to this phenomenon was that traffic can be approximated by a large number of ON/OFF sources where the random ON and/or OFF periods are of length described by a heavy-tailed distribution. In this paper we show that this argument is not necessary to explain self-similarity, neither is randomness is required. Rather, TCP itself as a deterministic process creates chaos, which generates self-similarity. This property is inherent in today's TCP/IP networks and it is independent of higher layer applications or protocols. The two causes, heavy-tailed ON/OFF and chaotic TCP together contribute to the phenomenon, called the fractal nature of Internet traffic.