The longest chapter in the Bible is Psalm 119. The shortest is Psalm 117. The middle of the bible can be found in Psalm 118.
There are actually a number of unusual coincidences surrounding Psalm 118. For instance, there are 1189 chapters in the Bible. That means that the middle chapter is the 595th chapter, Psalm 117.
What about the middle verse? According to Snopes, there are 31,174 verses in the Bible. Therefore, the middle verses are the 15,587th and 15,588th. Interestingly enough, those verses are verses 8 and 9 in Psalm 118. Also, the notation for verse 9 in Psalm 118 is Psalms 118:9, which is the same number as the total number of chapters in the Bible, 1189.
What does this all mean? Probably nothing. These coincidences only work for the King James version of the Bible, which isn't the only Bible out there. And when dealing with a book with this many numbers in it, interesting coincidences are bound to come up.
Still, if you think Psalm 118:9 must have some special significance you can read it here and learn more coincidences in the book of Psalms, courtesy of Snopes.