I assume you mean eastern/northern Limburg. Southern Liburg IS part of Belgium.
Originally Belgium claimed the nine southern provinces of the Kingdom of the Netherlands (East- and West-Flanders, South Brabant, Antwerp, Hainaut, Namur Liège, Luxembourg and Limburg), which would look like [this] (http://upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Belgique_1830.jpg/800px-Belgique_1830.jpg).
After the [Treaty of London] (http://en.wikipedia.org/wiki/Treaty_of_London_(1839)) in 1839 Belgium had to give up eastern Limburg and eastern Luxemburg (what is now known as the [Grand-Duchy of Luxembourg] (http://en.wikipedia.org/wiki/Luxembourg)) to get recognised by the Netherlands. It was basicly a compromise.
More sources:
Sorry for Wikipedia, I couldn't find any good English sources immediatly.
