Exhibit 3.117

State of Delaware

Secretary of State

Division of Corporations

Delivered 06:19 PM 12/20/2013

FILED 06:13 PM 12/20/2013

SRV 131462454 – 5454163 FILE

CERTIFICATE OF FORMATION

OF

TK BEHAVIORAL HOLDING COMPANY, LLC

Pursuant to Section 18-201 of the Delaware Limited Liability Company Act (the “Act”), the undersigned, desiring to form a limited liability company, does hereby certify as follows:

1. The name of the limited liability company is TK Behavioral Holding Company, LLC (the “Company”).

2. The address of the Company’s registered office in the State of Delaware is Corporation Trust Center, 1209 Orange Street, Wilmington, DE 19801. The name of the registered agent is The Corporation Trust Company.

3. This Certificate of Formation shall be effective upon filing with the Delaware Secretary of State.

IN WITNESS WHEREOF, the undersigned has executed this Certificate of Formation on this 20^th of December, 2013.

Christopher L. Howard, Authorized Person