Today's Montana Special Election Debate will be streamed online, beginning at 7:00 pm Mountain Time, with a Sunday MTPR rebroadcast, 6:00 pm. [NOTE: post timestamp altered to keep this item at top of postings]

MTPR posted, here, linking to Billings' KTVQ.com homepage.

http://www.ktvq.com/

If other outlets will livestream the event, none are known here at present.

Presumably an upload of the debate to YouTube shortly after the broadcast/rebroadcast is likely. Within days, hopefully.

UPDATE:
  Here, the KTVQ website says:

Saturday evening at 7 p.m. MTN will broadcast the first live candidate debate from the studios of KRTV in Great Falls, Mont.

Democrat Rob Quist, Republican Greg Gianforte, and Libertarian Mark Wicks will answer questions from a panel of MTN journalists including debate moderator and Q2 news anchor Jay Kohn.

The debate will be broadcast on all MTN stations including KTVQ and will be streamed live on all MTN websites including ktvq.com.