  We develop a Hamiltonian description of the `Carroll' (Levy Leblond-Sen
Gupta) limit of gravity theory in the first-order formalism. Through a
constraint analysis, the number of local degrees of freedom are shown to be two
in this singular limit. The associated Hamiltonian constraint depends only on
the densitized triad fields and their space derivatives. We also provide a
scaling prescription within the Hilbert-Palatini theory to obtain the
first-order analogue of the `electric' limit of canonical metric gravity. The
simplicity of both these limiting Hamiltonian forms in these variables make
them interesting candidates for quantization.
