Molybdenum disulfide (MoS2) is back in the spotlight because of the indirect-to-direct bandgap tunability and valley related physics emerging in the monolayer regime. However, rigorous control of the monolayer thickness is still a huge challenge for commonly utilized physical exfoliation and chemical synthesis methods. Herein, we have successfully grown predominantly monolayer MoS2 on an inert and nearly lattice-matching mica substrate by using a low-pressure chemical vapor deposition method. The growth is proposed to be mediated by an epitaxial mechanism, and the epitaxial monolayer MoS2 is intrinsically strained on mica due to a small adlayer-substrate lattice mismatch (~2.7%). Photoluminescence (PL) measurements indicate strong single-exciton emission in as-grown MoS2 and room-temperature PL helicity (circular polarization ~0.35) on transferred samples, providing straightforward proof of the high quality of the prepared monolayer crystals. The homogeneously strained high-quality monolayer MoS2 prepared in this study could competitively be exploited for a variety of future applications.