Whilst I agree with most of soapnuptys analysis, I do not agree a full structural survey will help. Such a survey considers what is visible, so the structural bit comprises examining what is visible of the superstructure and the construction of loadbearing elements. You would have to extend the normal scope plus have a builder dig a hole against to the walls to allow the surveyor to assess the depth and construction of the foundations. The normal depth of concrete for a house this age using a strip foundation would be one metre depth of concrete. But you should be able to find the dame information by asking at the Building Control office of your local council. There may be a fee.
However if it there is no sign of movement via minor hairline cracking in the walls, a surveyor will conclude that the foundations are stable.
I would be more interested in finding out what the soil is, because clay may well cause a problem. It is not an issue now (if no cracks), but future drying out of the soil as the tree grows could be. But worse could happen if the tree dies, as the clay would expand suddenly causing ground heave.
Other things to consider are whether this tree is in land you would own. If it is, at least you can request future crowning of the overall size via a planning application. Planners are not generally so unreasonable as to make people suffer if a TPO tree gets so big in relation to a nearby dwelling. However it you do not own this tree you will have no control on whether such an application can be made.
Finally, have you considered the above ground impact - loss of light throughout the summer, plus the need to remove a huge volume of leaves from gutters every autumn. Can you easily gain access to do this.
Chestnuts are mighty fine trees, but they grow very tall. Horse Chestnuts grow as wide as they are tall. Nine metres away doesn't sound far enough if I was buying it.