We report ab initio calculations of Al-27 NMR chemical shifts for a variety of Al(I) compounds using the gauge-including atomic orbital method at the self-consistent-field and second-order Moller-Plesset perturbation theory levels. The calculated values, which include one of the most shielded (AlCp) and deshielded (AlSitBu3) NMR shifts known so far for aluminum compounds, are rationalized in terms of a molecular orbital picture of the bonding and compared to the available experimental data for Al(I) compounds. For AlCl, it is shown that solvation effects have to be included in order to reproduce the experimental NMR shift of +35 ppm of a AlCl/toluene/ether solution, while for AlCp and AlCp* the Al-27 chemical shifts (-111 and -80.7 ppm, respectively) at low temperatures (<30-degrees-C) can be assigned on the basis of the calculated values to the tetramers Al4Cp4 and Al4Cp*4. Increasing the temperature above 30-degrees-C led in the case of the AlCp* solution to a new NMR signal at -149 ppm, which is in good agreement with the theoretically predicted value of -143 ppm for the AlCp* monomer. An analysis of the temperature-dependent NMR spectra yields an estimate of about 150 +/- 20 kJ/mol for the dissociation energy of Al4Cp*4 into four AlCp*. For AlCp, a similar analysis was, however, not possible due to the thermal instability of the AlCp solution, which decomposes above -60-degrees-C. No assignment of the experimentally observed Al-27 NMR spectrum has been so far possible in the case of AlSitBu3, but the calculations show that both solvation and electron correlation effects have to be included in a reliable theoretical study of the Al-27 chemical shifts of AlSiR3 compounds.