We demonstrate long-lived coherence in internal hyperfine states of a single Ca{43} trapped-ion qubit $[T_2=1.2(2)s]$, and in external motional states of a single Ca{40} trapped-ion qubit $[T_2=0.18(4)s]$, in the same apparatus. The motional decoherence rate is consistent with the heating rate, which was measured to be 3(1) quanta/sec. Long coherence times in the external motional states are essential for performing high-fidelity quantum logic gates between trapped-ion qubits. The internal-state $T_2$ time that we observe in Ca{43}, which has not previously been used as a trapped-ion qubit, is about one thousand times longer than that of physical qubits based on Ca{40} ions. Using a single spin-echo pulse to ``re-phase the internal state, we can detect no decoherence after 1s, implying an effective coherence time $T_2^{mbox{tiny SE}} gtish 45s$. This compares with timescales in this trap for single-qubit operations of ish 1us, and for two-qubit operations of ish 10us.
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