Designing effective software architectures is a complex, iterative process that traditionally relies on expert judgment. This paper proposes an approach for Large Language Model (LLM)-assisted software architecture design using the Attribute-Driven Design (ADD) method. By providing an LLM with an explicit description of ADD, an architect persona, and a structured iteration plan, our method guides the LLM to collaboratively produce architecture artifacts with a human architect. We validate the approach through case studies, comparing generated designs against proven solutions and evaluating them with professional architects. Results show that our LLM-assisted ADD process can generate architectures closely aligned with established solutions and partially satisfying architectural drivers, highlighting both the promise and current limitations of using LLMs in architecture design. Our findings emphasize the importance of human oversight and iterative refinement when leveraging LLMs in this domain.