In this paper, a dual-wavelength chaotic light source is proposed and demonstrated based on a fiber ring laser (FRL) with a semiconductor optical amplifier (SOA) as the intra-cavity gain element. By properly adjusting the bias current and the polarization, the SOA-FRL generates a high-dimension chaotic optical output with 24-nm optical bandwidth. The temporal instability of the output originates from the optical feedback, as well as the nonlinear effects of both the SOA and the long fiber. With optical-to-electrical conversion, the output electrical signal presents a bandwidth of 13 GHz, which is only limited by the bandwidth of the detection system. By inserting a tunable bandpass filter (TBPF) into the cavity, the chaotic emission bandwidth is limited to 3.2 nm. The output is then divided into two parallel channels using a wavelength division multiplexer (WDM). Autocorrelation of the two outputs confirms fair randomness, while the cross-correlation result verifies the independence of the two. With multi-bit sampling and over-sampling, dual-channel true random number generation (TRNG) up to 960 Gbps per channel is achieved. Random sampling periods are adopted to reduce the influence of the time-delay signature (TDS), which originates from the round-trip delay of the laser cavity and affects the randomness of the output. At a significance level of 0.01 and a random sampling ratio of 10-4 , the generated random bits can pass all the tests provided by the NITS SP800-22 test tool.