The theory that raising children in a multilingual environment impaired development was common in the 70s, but since then an overwhelming amount of evidence has debunked it. The commonly held view now is that raising a child in a multilingual environment will have no impact on how fast the child reaches developmental milestones.

A good introduction to the topic from Paul Bloom (a professor of developmental psychology at Yale) is here: http://oyc.yale.edu/psychology/psyc-110/lecture-6.