We present results of an intensive 2 month campaign of ground-based spectrophotometric monitoring of the Seyfert 1 galaxy NGC 7469, with a temporal resolution 1 day. The broad Hα and Hβ emission lines respond to ~35% ultraviolet continuum variations with an amplitude of ~10% and time delays of 5.6 ± 1.3 days and 5.4 ± 0.8 days, respectively. We interpret this as evidence of variable Balmer line gas ~5-6 light days from the central source in this object, widely believed to be a supermassive black hole. The virial mass of the central source implied by line widths and time delays is ~106-107 M☉. Concomitantly, we find evidence for wavelength-dependent continuum time delays: optical continuum variations lag those at 1315 Å by 1.0 ± 0.3 days at 4865 Å to 1.5 ± 0.7 days at 6962 Å. This suggests a stratified continuum reprocessing region extending several light days from the central source, possibly an accretion disk.