We have the authority to ask for anything because Jesus Christ is our representative in heaven, and we are his representative here on earth:
"Herein is our love made perfect, that we may have boldness in the day of
judgment: because as he is, so are we in this world." (1 John 4: 17)
We bear His Name and His Life within us -- how much more do we need to know and believe that we have every right to come before Him and ask for what we need.
However, let's take a closer look at the Prayer of Jabez. Through the Finished Work of Jesus Christ, we no longer have to exhort God to bless us, but rather we can rejoice in the Work that He has done and walk in the faith that He is working in us (Philippians 2: 12-13):
"And Jabez was
more honourable than his brethren: and his mother called his name Jabez, saying,
Because I bare him with sorrow.
called on the God of Israel, saying, Oh that thou wouldest bless me indeed, and
enlarge my coast, and that thine hand might be with me, and that thou wouldest
keep me from evil, that it may not grieve me! And God granted him that
which he requested." (1 Chronicles 4: 9-10)
A few notes about the translations. In verse 9, it would more accurately read "became honorable" -- he was not honorable just because, for in the God's presence no flesh will be justified.
How did Abraham become righteous? By praying a big prayer? By praying it a bunch of times? Not at all:
"And he brought him
forth abroad, and said, Look now toward heaven, and tell the stars, if thou be
able to number them: and he said unto him, So shall thy seed be.
he believed in the LORD; and he counted it to him for righteousness." (Genesis 15: 5-6)
Why did he become honorable (lit. glorious, weighed with honor? Because Jabez trusted God enough to ask Him for the most and the best -- yet for believers, He still outdoes the biggest requests that we can ask:
"Now unto him that
is able to do exceeding abundantly above all that we ask or think, according to
the power that worketh in us,
"Unto him be
glory in the church by Christ Jesus throughout all ages, world without end.
Amen.(Ephesians 3: 20-21)
So so not be discouraged if God does not give you what you initially requested, for He has something better in store for you. Ask, and you shall receive! (Matthew 7: 14)