Time series are commonly unevenly spaced in time make it difficult to obtain an accurate estimate of their typical red-noise spectrum. REDFIT overcomes this problem by fitting a first-order autoregressive (AR1) process directly to unevenly spaced time series. Hence, interpolation in the time domain and its inevitable bias can be avoided. The program can be used to test if peaks in the spectrum of a time series are significant against the red-noise background from an AR1 process.