We present a survey of the [CII] 158 $mu$m line and underlying far-infrared (FIR) dust continuum emission in a sample of 27 z>6 quasars using the Atacama Large Millimeter Array (ALMA) at ~1 resolution. The [CII] line was significantly detected (at >5-sigma) in 23 sources (85%). We find typical line luminosities of $L_{rm [CII]}=10^{9-10}$ L$_odot$, and an average line width of ~385 km/s. The [CII]-to-far-infrared luminosity ratio ([CII]/FIR) in our sources span one order of magnitude, highlighting a variety of conditions in the star-forming medium. Four quasar host galaxies are clearly resolved in their [CII] emission on a few kpc scales. Basic estimates of the dynamical masses of the host galaxies give masses between $2times10^{10}$ and $2times10^{11}$ M$_odot$, i.e., more than an order of magnitude below what is expected from local scaling relations, given the available limits on the masses of the central black holes ($>3times10^8$ M$_odot$, assuming Eddington-limited accretion). In stacked ALMA [CII] spectra of individual sources in our sample, we find no evidence of a deviation from a single Gaussian profile. The quasar luminosity does not strongly correlate with either the [CII] luminosity or equivalent width. This survey (with typical on-source integration times of 8 min) showcases the unparalleled sensitivity of ALMA at millimeter wavelengths, and offers a unique reference sample for the study of the first massive galaxies in the universe.