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We present the results from a narrow-band imaging survey for emission-line objects at high redshift using a Fabry-Perot interferometer. Specifically, this survey was designed to detect Ly$\alpha$ emission from young and possibly forming galaxies. A total of 12 ``blank'' fields were imaged with a useful field size of $\sim$5 arcmin square, 7 in the approximate redshift range 4.75-4.89, 3 in the range 4.42-4.60, and one each in the ranges 3.16-3.27 and 2.80-2.98. A total comoving volume of nearly 150,000 Mpc$^3$ was surveyed (H$ _0 =$ 75, $\Omega_0 =$ 0.2) to a line flux level deep enough to detect L$^*$ galaxies with 1\% of their bolometric luminosity in the Ly$\alpha$ line. Using the local space density of galaxies, this is a sufficient volume to have detected about 1000 L$^*$ galaxies. While none of the galaxies for which we have follow-up spectroscopy show definite Ly$\alpha$ emission, several interesting candidates do exist, as well as a fair number which still await a first spectroscopic observation. Lack of detection of strong Ly$\alpha$ emission from a population of primeval galaxies in this and similar surveys imply that either 1) galaxy formation was an inherently dusty process and UV photons, especially Ly$\alpha$, are easily destroyed, or 2) galaxy formation took place at different redshifts than can easily be surveyd with optical instruments, or 3) galaxy formation takes place via some other process than the model used for the design of this experiment (formation of the majority of a galaxy's stellar population in one or two freefall times $\sim10^8$ yr). Most of the candidates for which we have a spectroscopically confirmed, FP-selected emission-line are galaxies at $z\sim0.3-1$, possibly representative of the faint blue galaxies seen in the deep field surveys by Tyson, Cowie, Lilly, and others.
