We show that CERN LHC experiments might well be able to determine all the parameters required for a prediction of the present density of thermal LSP relics from the big bang era. If the LSP is an almost pure $B\ensuremath{-}\mathrm{i}\mathrm{n}\mathrm{o}$ we usually only need to determine its mass and the mass of the $\mathrm{SU}(2)$ singlet sleptons. This information can be obtained by reconstructing the cascade ${q}_{L}\ensuremath{\rightarrow}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{2}^{0}\stackrel{\ensuremath{\rightarrow}}{q}{l}_{R}l\stackrel{\ensuremath{\rightarrow}}{q}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{1}^{0}{l}^{+}{l}^{\ensuremath{-}}q.$ The only requirement is that ${m}_{{l}_{R}}l{m}_{{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{2}^{0}},$ which is true for most of the cosmologically interesting parameter space. If the LSP has a significant Higgsino component, its predicted thermal relic density is smaller than for an equal-mass $B\ensuremath{-}\mathrm{i}\mathrm{n}\mathrm{o}.$ We show that in this case squark decays also produce significant numbers of ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{4}^{0}$ and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{2}^{\ifmmode\pm\else\textpm\fi{}}.$ Reconstructing the corresponding decay cascades then allows us to determine the Higgsino component of the LSP.