Levi-Civita connection of a left-invariant metric

How do I compute Levi-Civita connection of a left-invariant metric on a Lie group in a neighbourhood of $1$ by knowing only its Lie algebra and the metric form on it? I know it's possible because a Lie group is determined by its Lie algebra in some small neighbourhood of $1$, but I just found out that I forgot how to compute Levi-Civita connection in this case in practice :) Is there some nice formula for this?

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Use the Koszul formula applied to left invariant vector fields. –  Jason DeVito Apr 22 '11 at 3:36
@JasonDeVito: can you please make your comment an answer so that I could accept it? –  Alexei Averchenko Oct 2 '11 at 9:30