diff --git a/cirq/sim/clifford/clifford_simulator.py b/cirq/sim/clifford/clifford_simulator.py
index 0b8a2311bd6..f38c0e6d179 100644
--- a/cirq/sim/clifford/clifford_simulator.py
+++ b/cirq/sim/clifford/clifford_simulator.py
@@ -370,8 +370,7 @@ def perform_measurement(
             state = self.copy()
 
         for qubit in qubits:
-            result = state.tableau._measure(self.qubit_map[qubit], prng)
-            state.ch_form.project_Z(self.qubit_map[qubit], result)
+            result = state.ch_form._measure(self.qubit_map[qubit], prng)
             results.append(result)
 
         return results
diff --git a/cirq/sim/clifford/stabilizer_state_ch_form.py b/cirq/sim/clifford/stabilizer_state_ch_form.py
index f5b597adc03..7e1b8ba8bcd 100644
--- a/cirq/sim/clifford/stabilizer_state_ch_form.py
+++ b/cirq/sim/clifford/stabilizer_state_ch_form.py
@@ -243,6 +243,22 @@ def to_state_vector(self) -> np.ndarray:
 
         return arr
 
+    def _measure(self, q, prng: np.random.RandomState) -> int:
+        """Measures the q'th qubit.
+
+        Reference: Section 4.1 "Simulating measurements"
+
+        Returns: Computational basis measurement as 0 or 1.
+        """
+        w = self.s.copy()
+        for i, v_i in enumerate(self.v):
+            if v_i == 1:
+                w[i] = bool(prng.randint(2))
+        x_i = sum(w & self.G[q, :]) % 2
+        # Project the state to the above measurement outcome.
+        self.project_Z(q, x_i)
+        return x_i
+
     def project_Z(self, q, z):
         """Applies a Z projector on the q'th qubit.
 
diff --git a/cirq/sim/clifford/stabilizer_state_ch_form_test.py b/cirq/sim/clifford/stabilizer_state_ch_form_test.py
index dfce42acee9..2007f9ffe91 100644
--- a/cirq/sim/clifford/stabilizer_state_ch_form_test.py
+++ b/cirq/sim/clifford/stabilizer_state_ch_form_test.py
@@ -36,3 +36,41 @@ def test_initial_state():
     expected_state_vector = np.zeros(32)
     expected_state_vector[23] = 1
     np.testing.assert_allclose(state.state_vector(), expected_state_vector)
+
+
+def test_run():
+    (q0, q1, q2) = (cirq.LineQubit(0), cirq.LineQubit(1), cirq.LineQubit(2))
+
+    """
+    0: ───H───@───────────────X───M───────────
+              │
+    1: ───────X───@───────X───────────X───M───
+                  │                   │
+    2: ───────────X───M───────────────@───────
+
+    After the third moment, before the measurement, the state is |000> + |111>.
+    After measurement of q2, q0 and q1 both get a bit flip, so the q0
+    measurement always yields opposite of the q2 measurement. q1 has an
+    additional controlled not from q2, making it yield 1 always when measured.
+    If there were no measurements in the circuit, the final state would be
+    |110> + |011>.
+    """
+    circuit = cirq.Circuit(
+        cirq.H(q0),
+        cirq.CNOT(q0, q1),
+        cirq.CNOT(q1, q2),
+        cirq.measure(q2),
+        cirq.X(q1),
+        cirq.X(q0),
+        cirq.measure(q0),
+        cirq.CNOT(q2, q1),
+        cirq.measure(q1),
+        strategy=cirq.InsertStrategy.NEW,
+    )
+    # CliffordSimulator uses StabilizerStateChForm internally.
+    # TODO: Use StabilizerStateChForm directly through `act_on` once
+    #  MeasurementGate is updated to use `_measure` from StabilizerStateChForm.
+    simulator = cirq.CliffordSimulator()
+    result = simulator.run(circuit, repetitions=10)
+    assert all(result.measurements['1'] == 1)
+    assert all(result.measurements['0'] != result.measurements['2'])