  We show that the Bousfield-Kan spectral sequence which computes the rational
homotopy groups of the space of long knots in ${\mathbb R}^d$, where $d\ge 4$,
collapses at the $E^2$ page. The main ingredients in the proof are Sinha's
cosimplicial model for the space of long knots and a coformality result for the
little balls operad.
