Recently published theoretical predictions by Pachucki and Yerokhin are in good agreement with the most precise measurements of helium fine structure and, for the first time, represent a complete calculation up to and including terms of order $\alpha^7$. In addition to serving as a test of this theory, more precise measurements could also yield a new determination of the fine structure constant $\alpha$ using atomic fine structure. A determination of $\alpha$ using helium fine structure was originally suggested by Charles Schwartz in a 1964 paper as a possible successor to the hydrogen determination. However, first the Josephson Effect and subsequently other methods superseded this approach, and only now can we again realize a competitive value for $\alpha$ using atomic fine structure. For my work, spectroscopic measurements of the helium atom are performed to high precision using an atomic beam apparatus and electro-optic laser techniques. With this setup, I have measured to 10 ppb the J = 0 to J = 2 fine structure interval in the $2^3p$ state of ${}_4{\rm He}$, yielding a precision to better than 5 ppb in $\alpha$. Outside the electron g factor determination, this is comparable in precision to the best alternative determinations of $\alpha$ obtained from photon recoil measurements in both Rb and Cs.