diff --git a/src/value/parse.rs b/src/value/parse.rs
index 34f2f73..354055f 100644
--- a/src/value/parse.rs
+++ b/src/value/parse.rs
@@ -647,7 +647,7 @@ impl Value {
                 };
                 let unit = if let Some(tok) = toks.peek() {
                     match tok.kind {
-                        'a'..='z' | 'A'..='Z' | '_' => {
+                        'a'..='z' | 'A'..='Z' | '_' | '\\' => {
                             let u = match eat_ident_no_interpolation(toks, true) {
                                 Ok(v) => v,
                                 Err(e) => return Some(Err(e)),
diff --git a/tests/units.rs b/tests/units.rs
index 5612fef..76c837e 100644
--- a/tests/units.rs
+++ b/tests/units.rs
@@ -74,6 +74,16 @@ test!(
     "a {\n  color: 1px-2px;\n}\n",
     "a {\n  color: -1px;\n}\n"
 );
+test!(
+    unit_starts_with_escape_sequence,
+    "a {\n  color: 1\\9;\n}\n",
+    "a {\n  color: 1\\9 ;\n}\n"
+);
+test!(
+    unit_fn_starts_with_escape_sequence,
+    "a {\n  color: unit(1\\9);\n}\n",
+    "a {\n  color: \"\\\\9 \";\n}\n"
+);
 error!(
     display_single_mul,
     "a {\n  color: 1rem * 1px;\n}\n", "Error: 1rem*px isn't a valid CSS value."