A Riemann-Hilbert problem is employed to study integrable three-component coupled Hirota (tcCH) equations. Thus, we investigate the spectral properties of tcCH equations with a 4 Ã— 4 Lax pair and derive a Riemann-Hilbert problem, the solution of which is used in constructing $N$-soliton solutions of the tcCH equations. While considering the spatiotemporal evolution of scattering data, the symmetry of the spectral problem is exploited. Graphical examples show new phenomena in soliton collision, including localised structures and dynamic behaviors of one- and two-soliton solutions. The results can be of interest in nonlinear dynamics of $N$-component nonlinear SchrÃ¶dinger type equations.