A process for the production of a high stereoregular polypropylene wherein(a) an isotactic pentad (m m m m) is 0.950 to 0.995,(b) a syndiotactic pentad (r r r r) is 0 to 0.01,(c) a different bond due to 2,1- and 1,3-insertions of propylene monomer is 0 to 0.3 mol %,(d) an absence of a terminal double bond is confirmed,(e) a weight average molecular weight (Mw) is 50,000 to 1,000,000 and(f) a ratio (Mw/Mn) of the weight average molecular weight (Mw) to a number average molecular weight (Mn) is 1.5 to 3.8, (a) to (d) being determined from .sup.13 C NMR spectra, comprising polymerizing propylene in the presence of hydrogen using a catalyst comprising a chiral transition metal compound and an aluminoxane, the transition metal compound being represented by the formula of Q(C.sub.5 H.sub.4-m R.sup.1.sub.m) (C.sub.5 H.sub.4-n R.sup.2.sub.n)MXY wherein (C.sub.5 H.sub.4-m R.sup.1.sub.m) and (C.sub.5 H.sub.4-n R.sup.2.sub.n) represent a substituted cyclopentadienyl group; m and n are an integer of 1 to 3; R.sup.1 and R.sup.2 may be the same or different and each represents an alkyl group of 1 to 20 carbons; Q is a group capable of crosslinking (C.sub.5 H.sub.4-m R.sup.1.sub.m) and (C.sub.5 H.sub.4-n R.sup.2.sub.n) and represents a divalent, hydrocarbyl radical, an unsubstituted silylene group or a hydrocarbyl-substituted silylene group; M represents a transition metal selected from the group consisting of titanium, zirconium, and hafnium; X and Y may be the same or different and each represents a hydrogen, a halogen or a hydrocarbyl radical, and wherein said polymerization is performed by a slurry polymerization using an aliphatic hydrocarbon as a solvent or by a bulk polymerization using propylene as a solvent.