We present details of the CARMA Large Area Star Formation Survey ( CLASSy ) , while focusing on observations of Barnard 1 . CLASSy is a CARMA Key Project that spectrally imaged N _ { 2 } H ^ { + } , HCO ^ { + } , and HCN ( J = 1 \rightarrow 0 transitions ) across over 800 square arcminutes of the Perseus and Serpens Molecular Clouds . The observations have angular resolution near 7 ^ { \prime \prime } and spectral resolution near 0.16 km s ^ { -1 } . We imaged \sim 150 square arcminutes of Barnard 1 , focusing on the main core , and the B1 Ridge and clumps to its southwest . N _ { 2 } H ^ { + } shows the strongest emission , with morphology similar to cool dust in the region , while HCO ^ { + } and HCN trace several molecular outflows from a collection of protostars in the main core . We identify a range of kinematic complexity , with N _ { 2 } H ^ { + } velocity dispersions ranging from \sim 0.05-0.50 km s ^ { -1 } across the field . Simultaneous continuum mapping at 3 mm reveals six compact object detections , three of which are new detections . A new , non-binary dendrogram algorithm is used to analyze dense gas structures in the N _ { 2 } H ^ { + } position-position-velocity ( PPV ) cube . The projected sizes of dendrogram-identified structures range from about 0.01-0.34 pc . Size-linewidth relations using those structures show that non-thermal line-of-sight velocity dispersion varies weakly with projected size , while rms variation in the centroid velocity rises steeply with projected size . Comparing these relations , we propose that all dense gas structures in Barnard 1 have comparable depths into the sky , around 0.1-0.2 pc ; this suggests that over-dense , parsec-scale regions within molecular clouds are better described as flattened structures rather than spherical collections of gas . Science-ready PPV cubes for Barnard 1 molecular emission are available for download .