  We study inflation driven by a dilaton and an axion, both of which are
coupled to a SU(2) gauge field. We find that the inflation driven by the
dilaton occurs in the early stage of inflation during which the gauge field
grows due to the gauge kinetic function. When the energy density of magnetic
fields catches up with that of electric fields, chromo-natural inflation takes
over in the late stage of inflation, which we call delayed chromo-natural
inflation. Thus, the delayed chromo-natural inflation driven by the axion and
the gauge field is induced by the dilaton. The interesting outcome of the model
is generation of chiral primordial gravitational waves on small scales. Since
the gauge field is inert in the early stage of inflation, it is viable in
contrast to the conventinal chromo-natural inflation. We find the parameter
region where chiral gravitational waves are generated in a frequency range
higher than nHz, which are potentially detectable in future gravitational wave
interferometers and pulsar timing arrays such as DECIGO, eLISA and SKA.
