Ancient Polynesian sailors are believed to have started sailing towards pacific islands with the intention to settle as early as 3000 BC from Asia. Given that some islands have hundreds of kilometres between each other that is an outstanding effort for such an ancient culture to travel in unpredictable seas. Though the Polynesians were impressive sailors they never had a civilisations per say, it was more so a collection of similar tribal cultures that vaguely knew of each other. To reach Easter island though is quite impressive.

If you are referring to a civilisation in the traditional sense probably the phoenicians as they started sailing across the Mediterranean in 1500 BC.

There's evidence that this is very ancient - specifically tuna bones have been found amongst fish-hooks in Timor, dated at 42kya. This strongly suggests mesolithic humans were regularly fishing well out to sea, at least in Sundaland. By that time, humans had also sailed to and populated Australia (c. 50kya).

This suggests that humans were confident sailors out at sea well before civilisation.

Source: http://m.livescience.com/17186-oldest-fish-hooks-early-humans.html