  We report an evidence for the first time that merging clusters of galaxies
are a promising candidate for the origin of high galactic-latitude, steady
unidentified EGRET gamma-ray sources. Instead of using past optical catalogs of
eye-selected clusters, we made a matched-filter survey of galaxy clusters over
$4\arcdeg \times 4\arcdeg$ areas around seven steady unidentified EGRET sources
at $|b|>45\arcdeg$ together with a 100 $\sq \arcdeg$ area near the South
Galactic Pole as a control field. In total, 154 Abell-like cluster candidates
and 18 close pairs/groups of these clusters, expected to be possibly merging
clusters, were identified within estimated redshift $z_{est}\leq 0.15$. Five
among the seven EGRET sources have one or two cluster pairs/groups (CPGs)
within 1$\arcdeg$ from them. We assess the statistical significance of this
result by several methods, and the confidence level of the real excess is
maximally 99.8% and 97.8% in a conservative method. In contrast, we found no
significant correlation with single clusters. In addition to the spatial
correlation, we also found that the richness of CPGs associated with EGRET
sources is considerably larger than those of CPGs in the control field. These
results imply that a part of the steady unidentified EGRET sources at
high-latitude are physically associated with close CPGs, not with single
clusters. We also discuss possible interpretations of these results. We argue
that, if these associations are real, they are difficult to explain by hadronic
processes, but best explained by the inverse-Compton scattering by high energy
electrons accelerated in shocks of cluster formation, as recently proposed.
