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We present measurements of anisotropy in the cosmic microwave background (CMB) from the first season of observations with the Degree Angular Scale Interferometer (DASI). The instrument was deployed at the South Pole in the austral summer 1999–2000, and we made observations throughout the following austral winter. We present a measurement of the CMB angular power spectrum in the range 100< l< 900 in nine bands with fractional uncertainties in the range 10%–20% and dominated by sample variance. In this paper, we review the formalism used in the analysis, in particular the use of constraint matrices to project out contaminants such as ground and point source signals and to test for correlations with diffuse foreground templates. We find no evidence of foregrounds other than point sources in the data, and we find a maximum likelihood temperature spectral index β=-0.1±0.2 (1 σ), consistent with CMB …