We present spectroscopic follow-up observations of CR7 with ALMA, targeted at constraining the infrared (IR) continuum and [C II](158 mu m) line-emission at high spatial resolution matched to the HST/WFC3 imaging. CR7 is a luminous Ly alpha emitting galaxy at z = 6.6 that consists of three separated UV-continuum components. Our observations reveal several well-separated components of [C II] emission. The two most luminous components in [C II] coincide with the brightest UV components (A and B), blueshifted by approximate to 150 km s(-1) with respect to the peak of Lya emission. Other [C II] components are observed close to UV clumps B and C and are blueshifted by approximate to 300 and approximate to 80 km s(-1) with respect to the systemic redshift. We do not detect FIR continuum emission due to dust with a 3 sigma limiting luminosity L-IR(T-d = 35 K) < 3.1 x 10(10) L-circle dot. This allows us to mitigate uncertainties in the dust-corrected SFR and derive SFRs for the three UV clumps A, B, and C of 28, 5, and 7 M-circle dot yr(-1). All clumps have [C II] luminosities consistent within the scatter observed in the local relation between SFR and L[C II], implying that strong Ly alpha emission does not necessarily anti-correlate with [C II] luminosity. Combining our measurements with the literature, we show that galaxies with blue UV slopes have weaker [C II] emission at fixed SFR, potentially due to their lower metallicities and/or higher photoionization. Comparison with hydrodynamical simulations suggests that CR7's clumps have metallicities of 0.1 < Z/Z(circle dot) < 0.2. The observed ISM structure of CR7 indicates that we are likely witnessing the build up of a central galaxy in the early universe through complex accretion of satellites.