diff --git a/include/mlir-hlo/Dialect/mhlo/IR/chlo_ops.td b/include/mlir-hlo/Dialect/mhlo/IR/chlo_ops.td
index c633bd2..68c641c 100644
--- a/include/mlir-hlo/Dialect/mhlo/IR/chlo_ops.td
+++ b/include/mlir-hlo/Dialect/mhlo/IR/chlo_ops.td
@@ -359,6 +359,20 @@ def HLOClient_AcosOp : HLOClient_UnaryElementwiseOp<"acos", [],
   }];
 }
 
+def HLOClient_AcoshOp : HLOClient_UnaryElementwiseOp<"acosh", [],
+    HLO_FpOrComplexTensor> {
+  let summary = "Acosh operation";
+
+  let description = [{
+    Returns `Acosh(operand)` element-wise.
+
+    $$
+    \acosh(x) = log(x + sqrt(x^2 - 1))      if x >= -1
+    \acosh(x) = nan                         if x < -1
+    $$
+  }];
+}
+
 def HLOClient_AsinOp : HLOClient_UnaryElementwiseOp<"asin", [],
     HLO_FpOrComplexTensor> {
   let summary = "Asin operator";
@@ -384,6 +398,7 @@ def HLOClient_AsinhOp : HLOClient_UnaryElementwiseOp<"asinh", [],
     $$
   }];
 }
+
 def HLOClient_AtanOp : HLOClient_UnaryElementwiseOp<"atan", [],
     HLO_FpOrComplexTensor> {
   let summary = "Atan operator";
diff --git a/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo_patterns.td b/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo_patterns.td
index a2b97a8..492e714 100644
--- a/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo_patterns.td
+++ b/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo_patterns.td
@@ -60,6 +60,58 @@ def : Pat<(HLOClient_AcosOp NonComplexElementType:$input),
     (HLO_ConstantLike<"M_PI"> $input)
   )>;
 
+// Expand acosh to MHLO dialect as follows:
+//   acosh(x) = log(x + sqrt(x^2 - 1))      if x >= -1
+//            = log(x + sqrt((x+1)*(x-1)))
+//   acosh(x) = nan                         if x < -1
+//
+// If x^2 will overflow, we approximate sqrt(x^2 - 1) == x and compute as
+// log(2*x) = log(2) + log(x).  (Note this works because negative x never
+// overflows; x < -1 simply yields nan.
+def : Pat<(HLOClient_AcoshOp NonComplexElementType:$input),
+  (HLO_SelectOp
+    (HLO_CompareOp
+      $input,
+      (HLO_ConstantLike<"-1"> $input),
+      HLO_COMPARISON_DIRECTION_LT,
+      (HLO_DEFAULT_COMPARISON_TYPE)
+    ),
+    (HLO_ConstantLike<"NAN"> $input),
+    (HLO_SelectOp
+      (HLO_CompareOp
+        $input,
+        (HLO_SqrtOp
+          (HLO_ConstantLikeMaxFiniteValue $input)
+        ),
+        HLO_COMPARISON_DIRECTION_GE,
+        (HLO_DEFAULT_COMPARISON_TYPE)
+      ),
+      (HLO_AddOp
+        (HLO_LogOp $input),
+        (HLO_LogOp
+          (HLO_ConstantLike<"2"> $input)
+        )
+      ),
+      (HLO_LogOp
+        (HLO_AddOp
+          $input,
+          (HLO_SqrtOp
+            (HLO_MulOp
+              (HLO_AddOp
+                (HLO_ConstantLike<"1"> $input),
+                $input
+              ),
+              (HLO_AddOp
+                (HLO_ConstantLike<"-1"> $input),
+                $input
+              )
+            )
+          )
+        )
+      )
+    )
+  )>;
+
 // Expand asin to MHLO dialect as follows:
 //   asin(x) = 2 * atan(x / (1 + sqrt(1 - x^2)))
 def : Pat<(HLOClient_AsinOp NonComplexElementType:$input),
diff --git a/lib/Dialect/mhlo/transforms/transform_unranked_hlo.cc b/lib/Dialect/mhlo/transforms/transform_unranked_hlo.cc
index b359217..063d077 100644
--- a/lib/Dialect/mhlo/transforms/transform_unranked_hlo.cc
+++ b/lib/Dialect/mhlo/transforms/transform_unranked_hlo.cc
@@ -51,9 +51,9 @@ namespace {
 
 // TODO(herhut): Generate these out of op definitions.
 #define MAP_CHLO_OPERATION_CWISE_UNARY(fn, sep)                            \
-  fn(AcosOp) sep fn(AsinOp) sep fn(AsinhOp) sep fn(AtanOp) sep fn(AtanhOp) \
-      sep fn(ConjOp) sep fn(CoshOp) sep fn(ErfOp) sep fn(ErfcOp)           \
-          sep fn(SinhOp) sep fn(TanOp)
+  fn(AcosOp) sep fn(AcoshOp) sep fn(AsinOp) sep fn(AsinhOp) sep fn(AtanOp) \
+      sep fn(AtanhOp) sep fn(ConjOp) sep fn(CoshOp) sep fn(ErfOp)          \
+          sep fn(ErfcOp) sep fn(SinhOp) sep fn(TanOp)
 
 template <typename OpTy>
 inline void AddLegalOpOnRankedTensor(ConversionTarget *target) {
diff --git a/tests/chlo_legalize_to_mhlo.mlir b/tests/chlo_legalize_to_mhlo.mlir
index 1a8613f..ccc9c92 100644
--- a/tests/chlo_legalize_to_mhlo.mlir
+++ b/tests/chlo_legalize_to_mhlo.mlir
@@ -171,3 +171,31 @@ func @erf_f16(%arg : tensor<f16>) -> tensor<f16> {
   %1 = "chlo.erf"(%arg) : (tensor<f16>) -> tensor<f16>
   return %1 : tensor<f16>
 }
+
+// CHECK-LABEL: @acosh
+// CHECK-SAME: %[[ARG:.*]]: tensor<f16>
+func @acosh(%arg: tensor<f16>) -> tensor<f16> {
+  // CHECK: %[[MINUSONE:.*]] = mhlo.constant dense<-1.000000e+00>
+  // CHECK: %[[CMP:.*]] = "mhlo.compare"(%[[ARG]], %[[MINUSONE]]) {comparison_direction = "LT"}
+  // CHECK: %[[MAX:.*]] = mhlo.constant dense<6.550400e+04>
+  // CHECK: %[[SQRTMAX:.*]] = "mhlo.sqrt"(%[[MAX]])
+  // CHECK: %[[OVERFLOW:.*]] = "mhlo.compare"(%[[ARG]], %[[SQRTMAX]]) {comparison_direction = "GE"}
+  // CHECK: %[[LOGARG:.*]] = "mhlo.log"(%[[ARG]])
+  // CHECK: %[[TWO:.*]] = mhlo.constant dense<2.000000e+00>
+  // CHECK: %[[LOGTWO:.*]] = "mhlo.log"(%[[TWO]])
+  // CHECK: %[[OFLRES:.*]] = mhlo.add %[[LOGARG]], %[[LOGTWO]]
+  // CHECK: %[[ONE:.*]] = mhlo.constant dense<1.000000e+00>
+  // CHECK: %[[ARGPONE:.*]] = mhlo.add %[[ONE]], %[[ARG]]
+  // CHECK: %[[MINUSONE2:.*]] = mhlo.constant dense<-1.000000e+00>
+  // CHECK: %[[ARGMONE:.*]] = mhlo.add %[[MINUSONE2]], %[[ARG]]
+  // CHECK: %[[MUL:.*]] = mhlo.multiply %[[ARGPONE]], %[[ARGMONE]]
+  // CHECK: %[[SQRT:.*]] = "mhlo.sqrt"(%[[MUL]])
+  // CHECK: %[[APSQRT:.*]] = mhlo.add %[[ARG]], %[[SQRT]]
+  // CHECK: %[[LOGAPMUL:.*]] = "mhlo.log"(%[[APSQRT]])
+  // CHECK: %[[SEL1:.*]] = "mhlo.select"(%[[OVERFLOW]], %[[OFLRES]], %[[LOGAPMUL]])
+  // CHECK: %[[NAN:.*]] = mhlo.constant dense<0x7E00>
+  // CHECK: %[[RESULT:.*]] = "mhlo.select"(%[[CMP]], %[[NAN]], %[[SEL1]])
+  // CHECK: return %[[RESULT]]
+  %1 = "chlo.acosh"(%arg) : (tensor<f16>) -> tensor<f16>
+  return %1 : tensor<f16>
+}