Hello Jason
If I have understood the facts correctly, the property/chalet is held by a company, and the proposed vendor is a member of the fund, where the asset that is proposed to be sold is the shares. It is assumed that the title in the chalet is held by way of company title.
This is discussed at paragraphs 109 – 112 of SMSFR 2009/1. Where the SMSF is purchase shares in such a scenario it still acquiring shares rather than the underlying property that the company owns.
Hence consideration needs to be given to the in-house asset rules and section 66 of the SIS Act  about acquiring assets from related parties.
As the shares are not listed the exception to acquiring assets from a related party in section 66(2)(a) does not apply.
However, if the shares will meet the requirements of section 71(1)(j) (and Regulations 13.22C and 13.22D) then the acquisition form a related party can be permitted under section 66(2A)(a)(iv). Amongst other things, to fall within this exception the company must not carry on a business, it was must not have any loans, it must not have any charges over its assets, it must not own interests in other entities, and if it is leasing an asset to a related party of the SMSF, the asset must be business real property.
Best regards
The Auditors Institute