Can brown eyed parents have a blue eyed baby

Yes, it is possible. 

However, this is only possible if BOTH of the parents have a recessive allele for blue eyes, i.e. they're heterozygous. 

Let only one gene is controllable of the eye color. Let the brown eye dominant allele be R and blue recessive be r. So, only if both parents have the genotypes of Rr, they can produce a baby with rr due to random selections at meiosis, and the baby phenotype would be blue eyed. 

If they're both RR or at least one is, the chance of having a blue-eyed baby is impossible.