We present an explicit pseudorandom generator for oblivious, read-once, width- 3 branching programs, which can read their input bits in any order. The generator has seed length O ( log 3 n ) The previously best known seed length for this model is n 1 2+ o (1) due to Impagliazzo, Meka, and Zuckerman (FOCS '12). Our work generalizes a recent result of Reingold, Steinke, and Vadhan (RANDOM '13) for \textit{permutation} branching programs. The main technical novelty underlying our generator is a new bound on the Fourier growth of width-3, oblivious, read-once branching programs. Specifically, we show that for any f : 0 1 n 0 1 computed by such a branching program, and k [ n ] s [ n ]: s = k f [ s ] n 2 ( O ( log n ) ) k where f [ s ] = E f [ U ] ( − 1 ) s U is the standard Fourier transform over Z n 2 . The base O ( log n ) of the Fourier growth is tight up to a factor of log log n .