  We evaluate the deuteron charge, quadrupole, and magnetic form factors using
wave functions obtained from chiral effective theory ($\chi$ET) when the
potential includes one-pion exchange, chiral two-pion exchange, and genuine
contact interactions. We study the manner in which the results for form factors
behave as the regulator is removed from the $\chi$ET calculation, and compare
co-ordinate- and momentum-space approaches. We show that, for both the LO and
NNLO chiral potential, results obtained by imposing boundary conditions in
co-ordinate space at $r=0$ are equivalent to the $\Lambda \to \infty$ limit of
momentum-space calculations. The regulator-independent predictions for deuteron
form factors that result from taking the $\Lambda \to \infty$ limit using the
LO $\chi$ET potential are in reasonable agreement with data up to momentum
transfers of order 600 MeV, provided that phenomenological information for
nucleon structure is employed. In this range the use of the NNLO $\chi$ET
potential results in only small changes to the LO predictions, and it improves
the description of the zero of the charge form factor.
