[en] The measurement of sparticle masses in the Minimal Supersymmetric Standard Model at the LHC is analysed, in the scenario where the lightest neutralino, the χ-tilde₁⁰ decays into three quarks. Such decays, occurring through the baryon-number violating coupling λ_iji^'', pose a severe challenge to the capability of the LHC detectors since the final state has no missing energy signature and a high jet multiplicity. We focus on the case λ₂₁₂^''≠0 which is the most difficult experimentally. The proposed method is valid over a wide range of SUGRA parameter space with λ'₂₁₂^''∼10^-5-0.1. Simulations are performed of the ATLAS detector at the Large Hadron Collider. Using the χ-tilde₁⁰ from the decay chain q-tilde_L→χ-tilde₂⁰q→l-tilde_rlq→χ-tilde₁⁰llq, we show that the χ-tilde₁⁰ and χ-tilde₂⁰ masses can be measured by 3-jet and 3-jet + lepton pair invariant mass combinations. At the SUGRA point m₀ 100 GeV, m_1/2 = 300 GeV, tan β = 10, μ >0 with λ₂₁₂^'' =0.005, we achieve statistical (systematic) errors of 3 (3), 3 (3), 0.3 (4) and 5 (12) GeV respectively for the masses of the χ-tilde₁⁰, χ-tilde₂⁰, l-tilde_r and q-tilde_L, with an integrated luminosity of 30 fb^-1. (author)