Edge excitations are the defining signature of chiral topologically ordered systems. In continuum fractional quantum Hall (FQH) states, these excitations are described by the chiral Luttinger liquid ($\chi \mathrm{LL}$) theory. Whether these field theory predictions can be precisely identified in discrete lattice systems of finite width, however, remains a long-standing question. Here, we numerically demonstrate that the charge-one edge spectral function of a $\nu =1/2$ fractional Chern insulator (FCI) on an infinitely long strip with width $L_y=10$ quantitatively follows the predictions of $\chi \mathrm{LL}$ theory. The edge spectrum is gapless, chiral, and linear, with spectral weight increasing linearly with both momentum and energy. We further analyze the influence of lattice size, particle number, trapping potential, and charge sector of excitations on the edge properties. Our results establish a clear correspondence between lattice FCIs and continuum FQH systems and provide guidance for future experimental detection of chiral edge modes.

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• Edge states
• Hall effect
• Topological order