This work uses Large Eddy Simulation (LES) combined with an accurate chemical description to predict soot formation in a turbulent spray flame burning real fuel at atmospheric conditions. Understanding and being able to predict soot formation in practical configurations burning complex liquid fuel is essential for the design of engines meeting present and future environmental requirements. The prediction of soot formation with numerical simulations has been mostly limited to academic configurations burning light gaseous fuel. This is explained by the numerical cost of (i) the fuel oxidation chemistry including soot precursors like Polycyclic Aromatic Hydrocarbons (PAH), and (ii) the modeling of two dispersed phases, i.e., the liquid fuel spray and the soot particles. In this work, an Analytically Reduced Chemistry (ARC) for real fuels is proposed to allow a direct integration of accurate combustion chemistry including PAH in the compressible LES solver AVBP. The ARC model is coupled with a Lagrangian particle tracking approach for both the fuel droplets and the soot, including for the latter the description of the complex physical and chemical processes driving the particle evolution. Validation is first performed in a one-dimensional ethylene/air flame configuration, experimentally studied in the literature at several operating points. The numerical profiles of both the soot volume fraction and the soot diameter are in good agreement with measurements. This allows to apply the LES methodology to the sooting swirled turbulent liquid JetA-1/air combustor measured at UTIAS. Very satisfying predictions for both the flow dynamics and the soot production are obtained. The analysis of the results brings valuable new insights on the interaction between fuel droplets, turbulent combustion, PAH and soot evolution in such complex flames.