In the following example: 

1) I bought a rental property in 2011 for $100,000 which has been fully rented since.

2) I transfered the property from myself to a single-member (myself) LLC in June 2017. The "sale" price was $1. The property was appraised at $150,000 at the time of LLC formation.

Determining depreciation before LLC formation was straight forward. How is this done for the LLC? Do I use the orriginal sale price that I, as an individual, bought it for? Sould depreciation for the property in the LLC start whan the property was transfered to the LLC?

You are a single member llc what was the purpose of "selling" the property to the llc?  All things being equal you just needed to re-title the property.  Disclaimer: As always, speak with your tax specialist about your specific situation.

You should consult your Tax Advisor but the transfer to the LLC should be disregarded for tax purposes since the transfer is to a disregarded entity (essentially a transfer to yourself). You would continue to depreciate the property as you did when you purchased it in 2011.

thanks for the replies. 

To clarify.  I transferred the property from my ownership to my llc as part of a loan based on the equity in the property. The lender required this for a commercial loan. My lawyer did the llc formation and all necessary title work.

@Nick G.

You will continue to report the property on schedule E and keep the basis that was reported on the 2011 return.
You should not adjust it based on the sale that occured between you and the LLC.