I have responsibility for students with alternate needs in my academic department (of a UK University). I also have responsibility for quality in teaching and learning. There are two issues that you raise here which are different, and being aware that they are different is necessary to understand routes to a solution.
There are different kinds of talking in class. There is the situation where two (or many) students are talking to each other whilst the teacher/lecturer continues with teaching. We teach in very large theatres (in hundreds) and this sometimes happens that the noise level at the back prevents students hearing the lecture, but the lecturer is unaware of the chatting until there is a complaint; or on some occasions the lecturer is aware of it and continue regardless!
There is the situation where the talking is from one student alone, either to themselves or chatting to you, interrupting you or asking questions of you with great regularity.
You have implied it is the one individual situation in your question, so I will constrain my answer to that situation specifically. One individual may be talking a lot for several reasons, some of which may be due to a specific condition. For example, a student with Tourette's may call out, involuntarily, and sometimes convert the interruption into a question to cover the situation. This is unlikely to be the position you have but I wanted to highlight it for others. This situation needs handling with some diplomacy and tact to avoid overly embarrassing yourself or the student in question. A student with Tourette's may appear overly aggressive or even acting improperly with respect to your gender. If this is the case you should seek advice from your special needs advisors.
A student on the Autistic Spectrum, which may include Asperger's, will relate to you differently an needs handling differently. For a student on the Autistic Spectrum they have more difficulty accepting that other people are present and see the class as a one-to-one conversation with you and treat it as such. They would respond to as if no one else was present. If you asked a rhetorical question, such as "What do we think of this?" - they will answer immediately! If you ask "Do we all understand" they will very likely say no (another aspect of Asperger's). One of my students used to answer his phone in class (quite loudly) because he had overlooked the fact that he was not alone.
Several things that a teacher can do with one (or more) student on the Autistic Spectrum in their class at University. We need to make it clear when question can be asked and when not. "I will explain how ..... and save any question until later. You can ask me questions after the end of class." is a simple statement that can make the protocol clearer. Avoid saying "Ask me any questions". They will take it literally, including asking non-related questions. If you want a Q&A session you again have to be clear: "I will take a small number of clarifying questions from different students." - this makes it clear that you cannot answer all the questions from one person and that the time is finite.
Once the protocol is clearly established such students are happy to work within such a regime. It is likely that it has never been explained to them how it works. Their condition makes it difficult to work it out for themselves how this aspect of human interaction operates. It has to be spelled out for them, even as adults and even at very high levels of knowledge. If you're not sure, watch a bit more of The Big Bang Theory!
A final note, that we also teach students with Psychosis which can manifest itself in various forms. This can include paranoia, delusional behaviour, threatening behaviour and so on. It can cause them to talk aloud in class (answering the voices they are hearing). Again, there may be gender related issues with this category of student and one should seek advice of the support professionals.
So, when in context, you can see that talking to the student in a quiet chat is a good place to start as you may learn the reason for their behaviour, but not all categories of "chatters" are necessarily self-aware. We have to remember that in many cases we are the responsible adult in the relationship (to use a legal term). The responsibility of doing the right thing is ours.