Romans 5:8 "But God demonstrates His own love toward us, in that while we were yet sinners, Christ died for us."

The love of God was shown because Christ died while we were yet sinners.  We were not worthy of the death of Christ, nothing we've ever done or will do merits us this kind of favor by God.  It was a complete demonstration of the unconditional, non-failing love of God.  It's the love described in 1 Corinthians 13, and in 1 John where God loved us first.

On another note, who is the us in this verse?  If we back up to Romans 5:1 Paul defines the pronouns of we/us with "Therefore, having been justified by faith, we have peace with God through our Lord Jesus Christ".  Those who Christ died for are the same as those who have been justified by God through faith.  A particular redemption of a particular people initiated by God to demonstrate His love and kindness.

Those who come to faith in Christ do so because God first loved them.