Ab initio G3(MP2,CC)//B3LYP/6-311G** calculations have been performed to investigate the potential energy surface (PES) and mechanism of the reaction of phenyl radical with propylene followed by kinetic RRKM-ME calculations of rate constants and product branching ratios at various temperatures and pressures. The reaction can proceed either by direct hydrogen abstraction producing benzene and three C(3)H(5) radicals [1-propenyl (CH(3)CHCH), 2-propenyl (CH(3)CCH(2)), and allyl (CH(2)CHCH(2))] or by addition of phenyl to the CH or CH(2) units of propylene followed by rearrangements on the C(9)H(11) PES producing nine different products after H or CH(3) losses. The H abstraction channels are found to be kinetically preferable at temperatures relevant to combustion and to contribute 55-75% to the total product yield in the 1000-2000 K temperature range, with the allyl radical being the major product (~45%). The relative contributions of phenyl addition channels are calculated to be ~35% at 1000 K, decreasing to ~15% at 2000 K, with styrene + CH(3) and 3-phenylpropene + H being the major products. Collisional stabilization of C(6)H(5) + C(3)H(6) addition complexes is computed to be significant only at temperatures up to 1000-1200 K, depending on the pressure, and maximizes at low temperatures of 300-700 K reaching up to 90% of the total product yield. At T > 1200 K collisional stabilization becomes negligible, whereas the dissociation products, styrene plus methyl and 3-phenylpropene + H, account for up to 45% of the total product yield. The production of bicyclic aromatic species including indane C(9)H(10) is found to be negligible at all studied conditions indicating that the phenyl addition to propylene cannot be a source of polycyclic aromatic hydrocarbons (PAH) on the C(9)H(11) PES. Alternatively, the formation of a PAH molecule, indene C(9)H(8), can be accomplished through secondary reactions after activation of a major product of the C(6)H(5) + C(3)H(6) addition reaction, 3-phenylpropene, by direct hydrogen abstraction by small radicals, such as H, OH, CH(3), etc. It is shown that at typical combustion temperatures 77-90% of C(9)H(9) radicals formed by H-abstraction from 3-phenylpropene undergo a closure of a cyclopentene ring via low barriers and then lose a hydrogen atom producing indene. This results in 7.0-14.5% yield of indene relative to the initial C(6)H(5) + C(3)H(6) reactants within the 1000-2000 K temperature range.