  Using a 281 pb^-1 data sample collected at the psi(3770) resonance with the
CLEO-c detector at the Cornell Electron Storage Ring, we report the first
observation of D^+ to eta e^+ nu_e. We also set upper limits for D^+ to eta'
e^+ nu_e and D^+ to phi e^+ nu_e that are about two orders of magnitude more
restrictive than those obtained by previous experiments.
