Chris,
Yes, this is possible. Assume TF1 *func the pointer to the function
you want to fit in TH1::Fit. Before calling TH1::Fit, do
func->SetParLimits(0,parlow,parhigh); //set bounds for all params
func->SetParLimits(1,...
then, specify the option "B" when calling TH1::Fit as specified
in the documentation of TH1::Fit
Rene Brun