We report the first theoretical study of transition-metal-catalyzed hydroalkoxylation of alkynes to produce enol ethers. The study utilizes density functional theory calculations (M06) to elucidate the mechanism and origins of Z selectivity of the anti-Markovnikov hydroalkoxylation of terminal alkynes with a Rh(I) 8-quinolinolato carbonyl chelate (1cat). The chosen system is, without any truncation, the realistic reaction of phenylacetylene and methanol with 1cat. Initiation of 1cat through phenylacetylene substitution for carbonyl generates the active catalyst, a Rh(I) η2-alkyne complex (3), which tautomerizes via an indirect 1,2-hydrogen shift to the Rh(I) vinylidene complex 4. The oxygen nucleophile methanol attacks the electrophilic vinylidene Cα, forming two stereoisomeric Rh(I) vinyl complexes (15 and 16), which ultimately lead to the (Z)- and (E)-enol ether products. These complexes undergo two ligand-mediated proton transfers to yield Rh(I) Fischer carbenes, which rearrange through a 1,2-β-hydrogen shift to afford complexes with π-bound product enol ethers. Final substitution of phenylacetylene gives (Z)- and (E)-PhCH-CHOMe and regenerates 3. The anti-Markovnikov regioselectivity stems from the Rh(I) vinylidene complex 4 with reversed Cα and Cβ polarity. The stereoselectivity arises from the turnover-limiting transition states (TSs) for the Rh(I) carbene rearrangement: the Z-product-forming TS24 is sterically less congested and hence more stable than the E-product-forming TS25. The difference in energy (1.2 kcal/mol) between TS24 and TS25 gives a theoretical Z selectivity that agrees well with the experimental value. Calculations were also performed on the key TSs of reactions involving two other alkyne substrates, and the results corroborate the proposed mechanism. The findings taken together give an insight into the roles of the rhodium-quinolinolato chelate framework in directing phenylacetylene attack by trans effect, mediating hydrogen transfers through hydrogen bonding, and differentiating the energies of key TSs by steric repulsion.