In August 2006, the CERN Theory Unit announced to restructure its visitor program and to create a 'CERN Theory Institute', where 1-3 month long specific programs can take place. The first such Institute was held from 14 May to 10 June 2007, focusing on 'Heavy Ion Collisions at the LHC - Last Call for Predictions'. It brought together close to 100 scientists working on the theory of ultra-relativistic heavy ion collisions. The aim of this workshop was to review and document the status of expectations and predictions for the heavy ion program at the Large Hadron Collider LHC before its start. LHC will explore heavy ion collisions at (almost equal to) 30 times higher center of mass energy than explored previously at the Relativistic Heavy Ion Collider RHIC. So, on the one hand, the charge of this workshop provided a natural forum for the exchange of the most recent ideas, and allowed to monitor how the understanding of heavy ion collisions has evolved in recent years with the data from RHIC, and with the preparation of the LHC experimental program. On the other hand, the workshop aimed at a documentation which helps to distinguish pre- from post-dictions. An analogous documentation of the 'Last Call for Predictions' [1] was prepared prior to the start of the heavy-ion program at the Relativistic Heavy Ion Collider RHIC, and it proved useful in the subsequent discussion and interpretation of RHIC data. The present write-up is the documentation of predictions for the LHC heavy ion program, received or presented during the CERN TH Institute. The set-up of the CERN TH Institute allowed us to aim for the wide-most coverage of predictions. There were more than 100 presentations and discussions during the workshop. Moreover, those unable to attend could still participate by submitting predictions in written form during the workshop. This followed the spirit that everybody interested in making a prediction had the right to be heard. To arrive at a concise document, we required that each prediction should be summarized on at most two pages, and that predictions should be presented, whenever possible, in figures which display measurable quantities. Full model descriptions were not accepted--the authors were encouraged to indicate the relevant references for the interested reader. Participants had the possibility to submit multiple contributions on different topics, but it was part of the subsequent editing process to ensure that predictions on neighboring topics were merged wherever possible. The contributions summarized here are organized in several sections, --though some of them contain material related with more than one section--roughly by going from low transverse momentum to high transverse momentum and from abundant to rare measurements. In the low transverse momentum regime, we start with predictions on multiplicity distributions, azimuthal asymmetries in particle production and hadronic flavor observables, followed by correlation and fluctuation measurements. The contributions on hard probes at the LHC start with predictions for single inclusive high transverse momentum spectra, and jets, followed by heavy quark and quarkonium measurements, leptonic probes and photons. A final section 'Others' encompasses those predictions which do not fall naturally within one of the above-mentioned categories, or discuss the more speculative phenomena that may be explored at the LHC.