  This paper describes the development of a threshold type aerogel Cherenkov
counter with a large sensitive area of 0.6 m$^2$ to be carried onboard the BESS
rigidity spectrometer to detect cosmic-ray antiprotons. The design incorporates
a large diffusion box containing 46 finemesh photomultipliers, with special
attention being paid to achieving good performance under a magnetic field and
providing sufficient endurance while minimizing material usage. The refractive
index of the aerogel was chosen to be 1.03. By utilizing the muons and protons
accumulated during the cosmic-ray measurements at sea level, a rejection factor
of 10$^4$ was obtained against muons with $\beta \approx 1$, while keeping 97%
efficiency for protons below the threshold.
