Neutron stars display phenomena which result from the burning of accreted nuclear fuel in their surface layers. In addition to producing X-ray bursts and other temporal phenomema, such burning can excite oscillation modes of the neutron star. Here we investigate the stability of R-modes in uniformly rotating neutron stars using nonadiabatic pulsation calculations of steady burning envelopes on accreting neutron stars. We find that the fundamental R-modes are unstable for a large range of accretion rates, and thus might manifest themselves observationally in the power spectra of accreting sources above about 1 kHz.