We report the results of a CGRO multi-instrument series of observations of the unidentified gamma-ray source 2CG 135+1 and of its possible counterpart, the peculiar radio source GT 0236+610 coincident with the Be star LSI +61 303. Previous observations of 2CG 135+1 are consistent with a positional coincidence of the gamma-ray source with LSI +61 303. Since January 1994, we continuously monitored the time variable radio source GT 0236+610 with the Green Bank Interferometer. For the first time, gamma-ray observations of 2CG 135+1 can be correlated with an extensive database of radio observations of LSI +61 303. We present OSSE and COMPTEL data obtained during the period May-June 1994, and BATSE data for the period April 1994-January 1995. We discuss the possible time variability of the γ-ray emission and spectral properties of 2CG 135+1. Understanding the nature of 2CG 135+1 may be of crucial importance for the interpretation of a class of unidentified and time variable gamma-ray sources in the Galaxy.