According to the regulator, Australian laws give consumers the right to cancel a lay-by agreement at any time before goods are delivered.
As well as this, the ACCC alleges from 2011 until this month the company charged people a termination fee that was more than its reasonable costs.
The regulator is seeking "pecuniary penalties, declarations, injunctions, non-party consumer redress and costs" from the company and the case is next due to come before the Federal Court in Brisbane in early February.
Chrisco Hampers Australia, directed by co-founder Richard Bradley, did not respond to a request for comment.
Bradley, who is understood to live in Australia, set up the lay-by hamper seller with his then-wife in New Zealand in 1993 after setting up a similar operation in Britain.
The Bradleys then expanded the business into Australia in 1997.
Asked if the hamper firm was being probed in New Zealand, a Commerce Commission spokesman told the Herald: "We aren't investigating Chrisco on anything at this time. We have just one recent complaint that is being looked at. Standard procedure is we receive a complaint and it goes to our screening team to assess whether the allegation requires investigation. A number of complaints fail screening as they don't meet the legal tests, so I can't say whether the current one has any grounds yet."