We report the observation of a correlation between shear Alfvén eigenmode activity and electron transport in plasma regimes where the electron temperature gradient is flat, and thus the drive for temperature gradient microinstabilities is absent. Plasmas having rapid central electron transport show intense, broadband global Alfvén eigenmode (GAE) activity in the 0.5-1.1 MHz range, while plasmas with low transport are essentially GAE-free. The first theoretical assessment of a GAE-electron transport connection indicates that overlapping modes can resonantly couple to the bulk thermal electrons and induce their stochastic diffusion. © 2009 The American Physical Society.