We present a 3mm spectral line and continuum survey of L1451 in the Perseus Molecular Cloud. These observations are from the CARMA Large Area Star Formation Survey (CLASSy), which also imaged Barnard 1, NGC1333, Serpens Main, and Serpens South. L1451 is the survey region with the lowest level of star formation activity-it contains no confirmed protostars. HCO^+^, HCN, and N_2_H^+^ (J=1->0) are all detected throughout the region, with HCO^+^ being the most spatially widespread, and molecular emission seen toward 90% of the area above N(H_2_) column densities of 1.9x10^21^cm^-2^. HCO^+^ has the broadest velocity dispersion, near 0.3km/s on average, compared with ~0.15km/s for the other molecules, thus representing a range of subsonic to supersonic gas motions. Our non-binary dendrogram analysis reveals that the dense gas traced by each molecule has a similar hierarchical structure, and that gas surrounding the candidate first hydrostatic core (FHSC), L1451-mm, and other previously detected single-dish continuum clumps has similar hierarchical structure; this suggests that different subregions of L1451 are fragmenting on the pathway to forming young stars. We determined that the three-dimensional morphology of the largest detectable dense-gas structures was relatively ellipsoidal compared with other CLASSy regions, which appeared more flattened at the largest scales. A virial analysis shows that the most centrally condensed dust structures are likely unstable against collapse. Additionally, we identify a new spherical, centrally condensed N_2_H^+^ feature that could be a new FHSC candidate. The overall results suggest that L1451 is a young region starting to form its generation of stars within turbulent, hierarchical structures.