Getting a DAC for this is not necessarily a solution unless you are certain that the digital output from the TV is PCM and not DolbyDigital. The vast majority of audio DACs will not decode DD and, therefore, will be of no help to you.
Any inexpensive, used AVR with digital input will do DD as will a few stand-alone devices, such as the Technics SH-AC500D decoder/DAC that I have in my closet (and would love to sell).
http://service.us.panasonic.com/OPERMANPDF/SHAC500D.PDFOtherwise, use the headphone output as Courant suggests. It is a cheap but effective solution.
Kal