Google and the Spokesman-Review have scanned and placed online a huge run of the Spokane Daily Chronicle. It appears that they have digitzed the paper from about 1890 through its demise in 1982. The articles are full text, searchable, and free. They are also deeply buried, so pay attention boys and girls.
The path to the newspapers is: Google News => Advanced News Search => Archive Search => Advanced Archive Search. At the last page, be sure that you enter Spokane in the "source" box.
I had a lot of fun trolling the archives for Spokane history, A search for "Chief Joseph" before 1920 (to screen out articles about Chief Joseph dam and such) turned up some wonderful primary sources, such as Old Foemen Met Again .Chief Joseph And General Howard Sat Side By Side--Famous Red Warrior Talks to Young Folks. The 1904 article reports

Surprisingly, the Chronicle seems not to have reported Joesph's death, which occurred on September 21, 1904, six months after his Carlisle speech.
Some other finds include this account a 1912 Spokane speech by Theodore Roosevelt, an 1898 story about a doctor arrested for performing an abortion, and a 1908 editorial about a development plan that would alter the falls on the Spokane Falls.
We are lucky indeed, as Spokane appears to be one of only a handful of cities available for free in the Google News archive. A bit of thrashing around in the archives reveals digitized historic content for St. Petersberg, Florida and a bunch of newspapers in New Zealand that seem to have been digitized as part of an independent project and are merely indexed via Google.
(Hat tip to the often-useful Eastern Washington Genealogical Society blog for discovering this resource.)