There are, at least, three artists named The Box.

1) A Montreal, Canada new wave band, formed 1981 by Jean-Marc Pisapia (an early member of Men Without Hats). The band was re-started, in 2003, with new lineup.
Originally, Jean-Marc recruited guitarist Guy Florent and bassist Jean-Pierre Brie for the band, who were originally known as Checkpoint Charlie before settling on the name The Box. After a 15-year hiatus the band released their fifth album, the progressive-rock flavored "Black Dog There" on Komfy-Universal. They released an all-French concept album in 2010 - "Le Horla De Maupassant" theBoxBand.com

2) Sheffield group 1981-1985, formed out of the ashes of the first Clock DVA. Former DVA members Paul Widger, Charlie Collins and Roger Quail linked up with bassman Terry Todd, and worked with several vocalists including Ken Bingley and Stephen Mallinder (of Cabaret Voltaire) before recruiting Peter Hope. The Box were the first group to sign for Go! Discs for whom they released 2 LPs and several singles. Parting company in 1984 they released further records on the Cabs' Doublevision imprint before splitting in 1985. Several members were later involved with the groups Flex 13, Pete Hope & The Jonathan S. Podmore Method and Hula.
Discography:
Secrets Out (UK Go! Discs, 1983)
The Box EP (UK Go! Discs, 1983)
Great Moments in Big Slam (UK Go! Discs, 1984)
Muscle In EP (UK Doublevision, 1985)
Muscle Out (UK Rough Trade, 1985)

3) AKA TACS, an MC/Producer from Oceanside,CA (San Diego) The core member of the short lived group PandorasBox, TACS is back as THE BOX with help from good friend and label mate Reason the Citizen. He is a firm believer in the DIY ethic.
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Artist biography from last.fm