# Relation between CLR Grammar and Ambiguity

I am studying CLR Parser and have a query about Grammar. If a Grammar can't be parsed using CLR(1) Parser ( i.e LR(1)) parser is it necessarily ambiguous?

Is it possible that a grammar which is unambiguous can't be parsed using CLR Parser?

For example the language $\{a^nb^n\mid n>0\}\cup\{a^nb^{2n}\mid n>0\}$. It is clearly unambiguous (it is easy to write an unambiguous grammar for it). But, informally, there is just no way you can decide which way you want to parse before you have read all the $a$ and as many $b$.