diff --git a/cue/format/testdata/expressions.txtar b/cue/format/testdata/expressions.txtar
index 02f79e0c6..063d14833 100644
--- a/cue/format/testdata/expressions.txtar
+++ b/cue/format/testdata/expressions.txtar
@@ -282,6 +282,20 @@ import "list"
     r: b & [1, 2, {a: 4}]
     s: [string]: [string]: a
     s: [string]: {s: string}
+
+    // Index expressions, including multi-line forms allowed via the
+    // optional trailing comma — see cuelang.org/issue/2738.
+    idx1: bar["baz"]
+    idx2: bar["baz",]
+    idx3: bar[
+        "baz"
+    ]
+    idx4: bar[
+        "baz",
+    ]
+    idx5: bar[foo[
+        "baz"
+    ]]
 }
 -- out/format/expressions.golden --
 package expressions
@@ -564,6 +578,20 @@ import "list"
 	r: b & [1, 2, {a: 4}]
 	s: [string]: [string]: a
 	s: [string]: {s: string}
+
+	// Index expressions, including multi-line forms allowed via the
+	// optional trailing comma — see cuelang.org/issue/2738.
+	idx1: bar["baz"]
+	idx2: bar["baz"]
+	idx3: bar[
+			"baz"
+			]
+	idx4: bar[
+			"baz"
+			]
+	idx5: bar[foo[
+			"baz"
+			]]
 }
 -- issue2496.input --
 machine_type: [
diff --git a/cue/parser/parser.go b/cue/parser/parser.go
index 771b12d11..8be14bf58 100644
--- a/cue/parser/parser.go
+++ b/cue/parser/parser.go
@@ -717,6 +717,9 @@ func (p *parser) parseIndexOrSlice(x ast.Expr) (expr ast.Expr) {
 			index[nColons] = p.parseRHS()
 		}
 	}
+	if nColons == 0 && p.tok == token.COMMA {
+		p.next()
+	}
 	p.exprLev--
 	rbrack := p.expect(token.RBRACK)
 
diff --git a/cue/parser/parser_test.go b/cue/parser/parser_test.go
index 18184a5e0..40bee274e 100644
--- a/cue/parser/parser_test.go
+++ b/cue/parser/parser_test.go
@@ -700,6 +700,18 @@ missing ',' in struct literal (and 1 more errors)`,
 		}`,
 			out: `@experiment(try), {a: {try {x: list[0]?}}}`,
 		},
+		{
+			desc: "index expression with trailing comma",
+			in:   `a: b["x",]`,
+			out:  `a: b["x"]`,
+		},
+		{
+			desc: "index expression with newline before closing bracket",
+			in: `a: b[
+				"x"
+			]`,
+			out: `a: b["x"]`,
+		},
 		{
 			desc:    "multiple else clauses error",
 			version: "v0.16.0",
diff --git a/doc/ref/spec.md b/doc/ref/spec.md
index 70f3a82db..6a6e6fd63 100644
--- a/doc/ref/spec.md
+++ b/doc/ref/spec.md
@@ -2067,7 +2067,7 @@ PrimaryExpr =
 	PrimaryExpr Arguments .
 
 Selector       = "." (identifier | simple_string_lit) .
-Index          = "[" Expression "]" .
+Index          = "[" Expression [ "," ] "]" .
 Argument       = Expression .
 Arguments      = "(" [ ( Argument { "," Argument } ) [ "," ] ] ")" .
 ```