  In this article, we prove the local well-posedness, for arbitrary initial
data with certain regularity assumptions, of the equations of a Viscoelastic
Fluid of Johnson-Segalman type with a free surface. More general constitutive
laws can be easily managed in the same way. The geometry is defined by a solid
fixed bottom and an upper free boundary submitted to surface tension. The proof
relies on a Lagrangian formulation. First we solve two intermediate problems
through a fixed point using mainly G. Allain Appl. Math. Optim. 16 (1987) 37-50
for the Navier-Stokes part. Then we solve the whole Lagrangian problem on
$[0,T_0]$ for $T_0$ small enough through a contraction mapping. Since the
Lagrangian solution is smooth, we can come back to an Eulerian one.
