ABSTRACT Any future detection of the calcium monohydroxide radical (CaOH) in stellar and exoplanetary atmospheres will rely on accurate molecular opacity data. Here, we present the first comprehensive molecular line list of CaOH covering the $\tilde{A}\, ^2\Pi$–$\tilde{X}\, ^2\Sigma ^+$ rotation-vibration-electronic and $\tilde{X}\, ^2\Sigma ^+$–$\tilde{X}\, ^2\Sigma ^+$ rotation-vibration bands. The newly computed OYT6 line list contains over 24.2 billion transitions between 3.2 million energy levels with rotational excitation up to J = 175.5. It is applicable to temperatures up to T = 3000 K and covers the 0–35 000 cm−1 range (wavelengths λ > 0.29 μm) for rotational, rotation-vibration and the $\tilde{A}\, ^2\Pi$–$\tilde{X}\, ^2\Sigma ^+$ electronic transitions. The strong band around 16 000 cm−1 (λ = 0.63 μm) is likely to be of interest in future astronomical observations, particularly in hot rocky exoplanets where temperatures can become extremely high. The OYT6 line list has been generated using empirically refined $\tilde{X}\, ^2\Sigma ^+$ and $\tilde{A}\, ^2\Pi$ state potential energy surfaces, high-level ab initio transition dipole moment surfaces, and a rigorous treatment of both Renner–Teller and spin-orbit coupling effects, which are necessary for correctly modelling the CaOH spectrum. Post-processing of the CaOH line list has been performed so as to tailor it to high-resolution applications, i.e. by replacing calculated energy levels with more accurate empirically derived values (where available), hence improving the accuracy of the predicted line positions in certain regions. The OYT6 line list is available from the ExoMol data base at www.exomol.com and the CDS astronomical data base.