This paper proposes a novel quantum computer based on ultracold polar molecules. The qubits are the electric dipole moments of diatomic molecules, oriented along or against an external electric field. The molecules are trapped in a 1-D optical lattice, with an electric field gradient allowing spectroscopic addressing of each site. The electric dipole-dipole interaction couples the bits. The design is feasible with existing technologies and can potentially achieve 10^4 qubits and perform 10^5 CNOT gates within a decoherence time of 5 seconds. The qubits are modeled as permanent electric dipoles oriented along or against an external electric field. The molecules are trapped in a 1-D optical lattice, with an electric field gradient allowing spectroscopic addressing of each site. The external field is perpendicular to the trap axis. The Hamiltonian for each bit includes the internal energy and the interaction with the external field. The internal field is created by the electric dipole moments of neighboring bits. Gate operations are performed using electric resonance, either directly in the microwave region or indirectly via optical stimulated Raman processes. Resonant drive pulses are tuned to a specific frequency. CNOT gates can be performed with pulses of sufficient temporal length to resolve the energy splitting due to the internal field. Final-state readout is achieved via state-selective, resonant multiphoton ionization and imaging detection. Ultracold diatomic molecules can be efficiently created by photoassociation of laser-cooled atoms. The molecules are formed at a translational temperature of about 20 μK. Production of ultracold atoms is most advanced for alkali atoms, and heteronuclear bi-alkali molecules are well suited for this purpose. The production rate of ultracold heteronuclear molecules is feasible, with a rate of >10^5/s. An optical trap is suitable for creating the desired 1-D array of molecules. The trap consists of a 1-D optical lattice superposed with a crossed dipole trap. The molecules are confined in sites spaced by λ_t/2. The trap depth is determined by the dynamic polarizability of the molecules. The trap parameters are chosen to ensure sufficient depth and stability. The system can achieve a high number of qubits and perform a large number of CNOT gates within the decoherence time. The system requires no dramatic breakthroughs for its initial construction. The electric resonance techniques for the processor are robust and easy to implement. The readout via resonance-enhanced ionization is standard. Unlike recent proposals for quantum computation using ultracold atoms, this technique requires neither mechanical motion nor coupling to short-lived excited states for gate operations. The system has potential for large-scale quantum computation and may be sufficient for quantum error correction methods to ensure stable computations. The paper also discusses potential improvements and other techniques that could enhance the system.This paper proposes a novel quantum computer based on ultracold polar molecules. The qubits are the electric dipole moments of diatomic molecules, oriented along or against an external electric field. The molecules are trapped in a 1-D optical lattice, with an electric field gradient allowing spectroscopic addressing of each site. The electric dipole-dipole interaction couples the bits. The design is feasible with existing technologies and can potentially achieve 10^4 qubits and perform 10^5 CNOT gates within a decoherence time of 5 seconds. The qubits are modeled as permanent electric dipoles oriented along or against an external electric field. The molecules are trapped in a 1-D optical lattice, with an electric field gradient allowing spectroscopic addressing of each site. The external field is perpendicular to the trap axis. The Hamiltonian for each bit includes the internal energy and the interaction with the external field. The internal field is created by the electric dipole moments of neighboring bits. Gate operations are performed using electric resonance, either directly in the microwave region or indirectly via optical stimulated Raman processes. Resonant drive pulses are tuned to a specific frequency. CNOT gates can be performed with pulses of sufficient temporal length to resolve the energy splitting due to the internal field. Final-state readout is achieved via state-selective, resonant multiphoton ionization and imaging detection. Ultracold diatomic molecules can be efficiently created by photoassociation of laser-cooled atoms. The molecules are formed at a translational temperature of about 20 μK. Production of ultracold atoms is most advanced for alkali atoms, and heteronuclear bi-alkali molecules are well suited for this purpose. The production rate of ultracold heteronuclear molecules is feasible, with a rate of >10^5/s. An optical trap is suitable for creating the desired 1-D array of molecules. The trap consists of a 1-D optical lattice superposed with a crossed dipole trap. The molecules are confined in sites spaced by λ_t/2. The trap depth is determined by the dynamic polarizability of the molecules. The trap parameters are chosen to ensure sufficient depth and stability. The system can achieve a high number of qubits and perform a large number of CNOT gates within the decoherence time. The system requires no dramatic breakthroughs for its initial construction. The electric resonance techniques for the processor are robust and easy to implement. The readout via resonance-enhanced ionization is standard. Unlike recent proposals for quantum computation using ultracold atoms, this technique requires neither mechanical motion nor coupling to short-lived excited states for gate operations. The system has potential for large-scale quantum computation and may be sufficient for quantum error correction methods to ensure stable computations. The paper also discusses potential improvements and other techniques that could enhance the system.