  Assuming the space dimension is not constant but decreases during the
expansion of the Universe, we study chaotic inflation with the potential $m^2
\phi^2/2$. We write down field equations in the slow-roll approximation and
define slow -roll parameters by assuming the space dimension to be a dynamical
parameter. The dynamical character of the space dimension shifts the initial
and final value of the inflaton field to larger values, producing delayed
chaotic inflation. We obtain an upper limit for the space dimension at the
Planck length. This result is in agreement with previous works on the effective
time variation of the Newtonian gravitational constant in a model Universe with
variable space dimensions. We present some cosmological consequences and
calculate observable quantities including the spectral indices, their
scale-dependence, and the mass of the inflaton field.
