We build inflationary models based on Degenerate Higher Order Scalar Tensor (DHOST) theories in a de Sitter background. We determine the power spectrum and bispectrum of curvature perturbations in such models. For the power spectrum, we find parameters matching the latest Planck measurements on the Cosmic Microwave Background (CMB). We show that the bispectrum consists of a contribution depending only on the power spectrum parameters and a linear combination of terms depending on new parameters, with the former peaking in the squeezed limit and the latter in the equilateral limit. We use the CMB-BEST code to directly confront the model predictions with the CMB bispectrum statistics, explicitly showing that there are parameter values satisfying both the power spectrum and bispectrum constraints. We show the limitations of using first order fudge factor approximations for non-Gaussianities.