I've never been given the chance before, but here's hoping it'll change. (Susan Boyle)

Is the above sentence grammatical?
Yes, it's grammatical. Here's hoping (that) is an idiom used to introduce a clause that expresses the speaker's strong desire, hope, or wish, especially just before the speaker makes an attempt to fulfill that hope. It's somewhat like I hope very much (that) ..., and here goes! (here goes! is itself an idiom that says "I'm about to try".)

00:00:05-00:00:04Hi, what's your name darling?
-My name is Susan Boyle
00:00:09-00:00:01Okay Susan, and where are you from?
00:00:11-00:00:02I am from Blackburn,
near Bathgate, West Lothian.
00:00:14-00:00:01That's a big town.
00:00:15-00:00:05It's a sort of collection of...
It's a collection of.. villages.
00:00:21-00:00:01Had to think there.

What does "Had to think there" mean?
Students: We have free audio pronunciation exercises.
sitifanWhat does "Had to think there" mean?
I had to think [just now / at that moment / in that case]. (The word villages did not easily come to mind for her. She was a little nervous, I suppose.)