Anastasia - when I read the Psalms, King David references several times how he rises early to pray - or he remembers the Lord even on his bed any time he wakes up through the night or when he first wakes up for the day.
Asteriktos is right - I don't think this is a law of some sort stating you should get up early to pray - but more of a frame work of where your heart is. . .do you drag yourself to prayer or do you go to bed at night and know you'll miss Him while you sleep and can't wait to be in His presence in prayer as SOON as you are able?
When my children were small - being able to pray meant sometime around lunch time, as this was the first opportunity I could actually pray with out interruption. . .and how I cherished that time, from the first moment. . . that was my morning.
Another way to look at is in petitions - "Ok, I know this is important, let's call the doctor first thing in the morning." Ever hear your mom say that? It's not a crisis, you don't need to go to the emergency room, but it' is a high priority and the doctor needs to be first on the list for phone calls because this need does need to have care as soon as possible. So in petitions, its a matter of knowing that it's a high priority that takes the 'first call in the morning' to our God.
It's a two way relationship. In Psalm 5 - King David says that in the morning God hears his voice. . .so he prays in the morning.
But, as Asteriktos said, it's not a thing that has to be done at a certain time. . .it's a 'first fruit', if you will, the moment you are aware you've had some time without Him in conscious thought - just like you would miss a lover for a time of separation. . . and knowing that the same is returned - as He hears us when we come to him with that longing. So it's a heart tone more than a heart 'time'.