  We investigate extra spatial dimensions ($D = 3+\epsilon$) in the early
universe using very high resolution molecular rotational spectroscopic data
derived from a large molecular cloud containing moderately cold carbon monoxide
gas at Z $\approx 6.42$. It turns out that the $\epsilon$-dependent quantum
mechanical wavelength transitions are solvable for a linear molecule and we
present the solution here. The CO microwave data allows a very precise
determination of $< \epsilon > = -0.00000657 \pm .10003032$. The probability
that $ < \epsilon > \neq 0$ is one in 7794, only 850 million years (using the
standard cosmology) after the Big Bang.
