The Chase will definitely get a season 4, and here's why:
Since 2011, no other GSN original has risen in viewers from premiere to the following episode like The Chase has. The Chase has risen a total of 15% week-to-week-to-week since the season premiere, with the July 8th premiere episode receiving 494,000 viewers, the second episode receiving 534,000 viewers on July 15th and the third receiving 578,000 viewers on July 22nd. No other show on Game Show Network has done this, or anything close, in recent history.
In 2011, The Newlywed Game and Love Triangle premieres both gained viewers from their season/series premiere to episode 2. The Newlywed Game Season 5 premiere, on April 18, 2011, gained a 1% audience from episode 1 to 2 (408K to 413K). The Newlywed Game was eventually renewed for a sixth season. The Love Triangle series premiere, on April 11, 2011, gained 5% in viewers from episode 1 to 2 (367K to 386K).
No other shows in recent GSN history have risen from season premiere to the following episode. The Newlywed Game and Love Triangle did not have the high ratings The Chase now has and in addition, the viewer growth that The Chase has had these past few weeks.
Additionally, Mark Labbett has turned into a very recognizable figure for GSN viewers, where Game Show Network is already tying The Chase into promoting Idiotest. GSN will continue to tie in future shows with The Chase if the show continues to average 500K+ viewers in the future like it has at the end of Season 1, Season 2 (average) and so far, Season 3.
Lastly, Brooke Burns is not leaving the show anytime soon, with multiple sources reporting she is tied-down to a multi-year contract with the show that she cannot opt out of so easily (please people, I am not the first person to know details, finances and longevity with host/Chaser contracts, but I do know this much.) Mark Labbett appears to enjoy The Chase as well, where The Chase is having zero problem casting with years worth of contestants to come.
I am positive, only three of thirteen episodes into the third season, without any status from GSN whether The Chase is renewed or not that we will see The Chase get a fourth season on Game Show Network.