BBH are the advertising agency that handled the Lynx account. BBH are the creatives behind the campaign. Like all advertising agencies, they hire a production company to actually make the ad. In this case, the ad was shot by the production company MJZ...
"The ad, called "the chain", was shot by Tom Kuntz, through production company MJZ, who has previously won awards for Cadbury's "eyebrows" ad and Old Spice's "the man your man can smell like" ad."