We report a rectangular charge density wave (CDW) phase in strained 1T-VSe2 thin films synthesized by molecular beam epitaxy on c-sapphire substrates. The observed CDW structure exhibits an unconventional rectangular 4a x root 3a periodicity, as opposed to the previously reported hexagonal 4a x 4a structure in bulk crystals and exfoliated thin-layered samples. Tunneling spectroscopy shows a strong modulation of the local density of states of the same 4a x root 3a CDW periodicity and an energy gap of 2 Lambda(CDW) = (9.1 +/- 0.1) meV. The CDW energy gap evolves into a full gap at temperatures below 500 mK, indicating a transition to an insulating phase at ultra-low temperatures. First-principles calculations confirm the stability of both 4a x 4a and 4a x root 3a structures arising from soft modes in the phonon dispersion. The unconventional structure becomes preferred in the presence of strain, in agreement with experimental findings.