diff --git a/racket/src/ChezScheme/mats/cptypes.ms b/racket/src/ChezScheme/mats/cptypes.ms
index a6827fb562..c680803001 100644
--- a/racket/src/ChezScheme/mats/cptypes.ms
+++ b/racket/src/ChezScheme/mats/cptypes.ms
@@ -198,6 +198,18 @@
   (cptypes-equivalent-expansion?
     '(lambda (x) (vector-set! x 0 0) (#2%odd? x) 1)
     '(lambda (x) (vector-set! x 0 0) (#2%odd? x) 2))
+  (cptypes-equivalent-expansion?
+    '(lambda (x) (when (or (fixnum? x) (bignum? x)) (zero? x)))
+    '(lambda (x) (when (or (fixnum? x) (bignum? x)) (#3%eq? x 0))))
+  (cptypes-equivalent-expansion?
+    '(lambda (x) (when (and (or (fixnum? x) (bignum? x)) (zero? x)) x))
+    '(lambda (x) (when (and (or (fixnum? x) (bignum? x)) (zero? x)) 0)))
+  (cptypes-equivalent-expansion?
+    '(lambda (x) (when (fixnum? x) (zero? x)))
+    '(lambda (x) (when (fixnum? x) (#3%fxzero? x))))
+  (cptypes-equivalent-expansion?
+    '(lambda (x) (when (and (fixnum? x) (zero? x)) x))
+    '(lambda (x) (when (and (fixnum? x) (zero? x)) 0)))
 )
 
 (mat cptypes-type-if
diff --git a/racket/src/ChezScheme/s/cptypes.ss b/racket/src/ChezScheme/s/cptypes.ss
index 15a3a84a71..9b343839f8 100644
--- a/racket/src/ChezScheme/s/cptypes.ss
+++ b/racket/src/ChezScheme/s/cptypes.ss
@@ -1073,6 +1073,40 @@ Notes:
                  [else
                   (values `(call ,preinfo ,pr ,n) ret ntypes #f #f)]))])
 
+      (define-specialize 2 zero?
+        [(n) (let ([r (get-type n)])
+               (cond
+                 [(predicate-implies? r 'bignum)
+                  (values (make-seq ctxt n false-rec)
+                          false-rec ntypes #f #f)]
+                 [(predicate-implies? r 'fixnum)
+                  (values `(call ,preinfo ,(lookup-primref 3 'fxzero?) ,n)
+                          ret
+                          ntypes
+                          (pred-env-add/ref ntypes n `(quote 0) plxc)
+                          #f)]
+                 [(predicate-implies? r 'exact-integer)
+                  (values `(call ,preinfo ,(lookup-primref 3 'eq?) ,n (quote 0))
+                          ret
+                          ntypes
+                          (pred-env-add/ref ntypes n `(quote 0) plxc)
+                          #f)]
+                 [(predicate-implies? r 'flonum)
+                  (values `(call ,preinfo ,(lookup-primref 3 'flzero?) ,n)
+                          ret
+                          ntypes
+                          #f ; TODO: Add a type for flzero
+                          #f)]
+                 [else
+                  (values `(call ,preinfo ,pr ,n) ret ntypes #f #f)]))])
+
+      (define-specialize 2 fxzero?
+        [(n) (values `(call ,preinfo ,pr ,n)
+                     ret
+                     ntypes
+                     (pred-env-add/ref ntypes n `(quote 0) plxc)
+                     #f)])
+
       (define-specialize 2 atan
         [(n) (let ([r (get-type n)])
                (cond
diff --git a/racket/src/ChezScheme/s/primdata.ss b/racket/src/ChezScheme/s/primdata.ss
index c9a6d015cb..4a7bfd039c 100644
--- a/racket/src/ChezScheme/s/primdata.ss
+++ b/racket/src/ChezScheme/s/primdata.ss
@@ -45,7 +45,7 @@
   (fx=? [sig [(fixnum fixnum fixnum ...) -> (boolean)]] [flags pure cp02 safeongoodargs])    ; restricted to 2+ arguments
   (fx>? [sig [(fixnum fixnum fixnum ...) -> (boolean)]] [flags pure cp02 safeongoodargs])    ; restricted to 2+ arguments
   (fx>=? [sig [(fixnum fixnum fixnum ...) -> (boolean)]] [flags pure cp02 safeongoodargs])   ; restricted to 2+ arguments
-  (fxzero? [sig [(fixnum) -> (boolean)]] [flags pure cp02 safeongoodargs])
+  (fxzero? [sig [(fixnum) -> (boolean)]] [flags pure cp02 safeongoodargs cptypes2])
   (fxnegative? [sig [(fixnum) -> (boolean)]] [flags pure cp02 safeongoodargs])
   (fxpositive? [sig [(fixnum) -> (boolean)]] [flags pure cp02 safeongoodargs])
   (fxeven? [sig [(fixnum) -> (boolean)]] [flags pure cp02 safeongoodargs])
@@ -201,7 +201,7 @@
   ((r6rs: =) [sig [(number number number ...) -> (boolean)]] [flags pure mifoldable discard safeongoodargs ieee r5rs])   ; restricted to 2+ arguments
   ((r6rs: >) [sig [(real real real ...) -> (boolean)]] [flags pure mifoldable discard safeongoodargs ieee r5rs])   ; restricted to 2+ arguments
   ((r6rs: >=) [sig [(real real real ...) -> (boolean)]] [flags pure mifoldable discard safeongoodargs ieee r5rs])  ; restricted to 2+ arguments
-  (zero? [sig [(number) -> (boolean)]] [flags pure mifoldable discard safeongoodargs ieee r5rs])
+  (zero? [sig [(number) -> (boolean)]] [flags pure mifoldable discard safeongoodargs cptypes2 ieee r5rs])
   (positive? [sig [(real) -> (boolean)]] [flags pure mifoldable discard safeongoodargs ieee r5rs])
   (negative? [sig [(real) -> (boolean)]] [flags pure mifoldable discard safeongoodargs ieee r5rs])
   (odd? [sig [(integer) -> (boolean)]] [flags pure mifoldable discard safeongoodargs ieee r5rs])