TITLE: $\aleph_2$ Suslin Hypothesis
QUESTION [7 upvotes]: Is it still open whether ZFC+GCH is consistent with the statement that there are no $\aleph_2$-Suslin trees?

REPLY [6 votes]: From http://www.users.muohio.edu/larsonpb/kly_guessing.pdf (pdf 9 of 16): 

Note that the consistency of GCH + "no $\omega_{2}$-Suslin-trees" is
  still an open question. ...this old question is now more open than
  ever.

As best as I can tell, the matter has not been settled in the six years since the published paper above.
Citation: 
König, B., Larson, P., & Yoshinobu, Y. (2007). Guessing clubs in the generalized club filter. Fundamenta Mathematicae, 195(2), 177-191.