  We build an inflationary model based on Degenerate Higher Order Scalar Tensor
(DHOST) theories in a de Sitter background. We determine the scale-dependent
power spectrum of curvature perturbations in these theories and we show that
such a model can be compatible with the latest Planck measurements on the
Cosmic Microwave Background (CMB). We calculate the bispectrum of curvature
perturbations in DHOST models and we directly constrain them using the Planck
results on non-Gaussianities. 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. The former peaks in the
squeezed limit, while the latter in the equilateral limit. We use the publicly
available CMB-BEST code to directly compare the model predictions to the CMB
bispectrum statistics and to marginalise over the free parameters, explicitly
showing that there are viable DHOST inflationary models that satisfy both the
power spectrum and bispectrum constraints from Planck.
