The recent discovery of two-dimensional (2D) ferromagnetism proves that magnetic anisotropy can overcome thermal fluctuations and stabilize long-range magnetic orders in the 2D limit at finite temperatures. This has immediately triggered tremendous interest in potential 2D magnet-based applications, ranging from ultra-thin magnetic sensors to high efficiency spin filter devices. Naturally, a complete description of the 2D magnetic phase is now needed, which requires not only the identification of the ordered ground state, but equally important, the understanding of the excitations, i.e., spin waves, or equivalently, magnons. Here, using polarized micro-Raman spectroscopy, we report the definitive evidence of two sets of zero-momentum spin waves in a 2D honeycomb ferromagnet CrI3 at frequencies of 2.28 and 3.75 THz, respectively, that are three orders of magnitude higher than those of the conventional ferromagnets (typically at GHz frequencies). Surprisingly, by tracking the layer number dependence of both spin waves, we notice that the integrated intensity of each magnon mode shows no thickness dependence, indicative of surface magnons. Moreover, we show that, from more than ten-layer to monolayer CrI3, the spin wave frequencies (2.28 and 3.75 THz) and their onset temperatures (45 K) remain nearly constant, while their lifetimes decrease significantly from 50 and 100 ps to 15 ps, but remaining an order of magnitude longer than their corresponding spin wave temporal periods. Our results of two branches of high-frequency and long-lived surface spin waves in the 2D Ising ferromagnet CrI3 demonstrate intriguing spin dynamics and intricate interplay with thermal fluctuations in the 2D limit, thus opening up new opportunities for ultrafast spintronics incorporating 2D magnets.