  The proximity of core-collapse Supernova 1987A (SN1987A) in the Large
Magellanic Cloud (LMC) and its rapid evolution make it a unique case study of
the development of a young supernova remnant. We aim at resolving the remnant
of SN1987A for the first time in the 3-mm band (at 94 GHz). We observed the
source at 3-mm wavelength with a 750-m configuration of the Australia Telescope
Compact Array (ATCA). We compare the image with a recent 3-cm image and with
archival X-ray images. We present a diffraction-limited image with a resolution
of 0.7", revealing the ring structure seen at lower frequencies and at other
wavebands. The emission peaks in the eastern part of the ring. The 3-mm image
bears resemblance to early X-ray images (from 1999-2000). We place an upper
limit of 1 mJy (2 \sigma) on any discrete source of emission in the centre
(inside of the ring). The integrated flux density at 3 mm has doubled over the
six years since the previous observations at 3 mm. At 3 mm - i.e. within the
operational domain of the Atacama Large Millimeter/submillimeter Array (ALMA) -
SN1987A appears to be dominated by synchrotron radiation from the inner rim of
the equatorial ring, characterised by moderately-weak shocks. There is no clear
sign of emission of a different nature, but the current limits do not rule out
such component altogether.
