diff --git a/tstime/tstime.go b/tstime/tstime.go
new file mode 100644
index 000000000..4867b7ff7
--- /dev/null
+++ b/tstime/tstime.go
@@ -0,0 +1,58 @@
+// Copyright (c) 2020 Tailscale Inc & AUTHORS All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package tstime defines Tailscale-specific time utilities.
+package tstime
+
+import (
+	"strings"
+	"sync"
+	"time"
+)
+
+// zoneOf returns the RFC3339 zone suffix, or the empty string
+// if it's invalid or not something we want to cache.
+func zoneOf(s string) string {
+	if strings.HasSuffix(s, "Z") {
+		return ""
+	}
+	if len(s) < len("2020-04-05T15:56:00+08:00") {
+		// Too short, invalid? Let time.Parse fail on it.
+		return ""
+	}
+	zone := s[len(s)-len("+08:00"):]
+	if c := zone[0]; c == '+' || c == '-' {
+		min := zone[len("+08:"):]
+		switch min {
+		case "00", "15", "30":
+			return zone
+		}
+	}
+	return ""
+}
+
+// locCache maps from zone offset suffix string ("+08:00") =>
+// *time.Location (from FixedLocation).
+var locCache sync.Map
+
+// Parse3339 is a wrapper around time.Parse(time.RFC3339Nano, s) that caches
+// timezone Locations for future parses.
+func Parse3339(s string) (time.Time, error) {
+	zone := zoneOf(s)
+	if zone == "" {
+		return time.Parse(time.RFC3339Nano, s)
+	}
+	loci, ok := locCache.Load(zone)
+	if ok {
+		// TODO(bradfitz): just rewrite this do the trivial parsing by hand
+		// which will be faster than Go's format-driven one. RFC3339 is trivial.
+		return time.ParseInLocation(time.RFC3339Nano, s, loci.(*time.Location))
+	}
+	t, err := time.Parse(time.RFC3339Nano, s)
+	if err != nil {
+		return time.Time{}, err
+	}
+	locCache.LoadOrStore(zone, t.Location())
+	return t, nil
+}
diff --git a/tstime/tstime_test.go b/tstime/tstime_test.go
new file mode 100644
index 000000000..a598cec42
--- /dev/null
+++ b/tstime/tstime_test.go
@@ -0,0 +1,104 @@
+// Copyright (c) 2020 Tailscale Inc & AUTHORS All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package tstime
+
+import (
+	"testing"
+	"time"
+)
+
+func TestZoneOf(t *testing.T) {
+	tests := []struct {
+		in, want string
+	}{
+		{"2020-04-05T15:56:00+08:00", "+08:00"},
+		{"2020-04-05T15:56:00-08:00", "-08:00"},
+		{"2020-04-05T15:56:00.12345-08:00", "-08:00"},
+		// don't cache weird offsets, only 00 15, 30:
+		{"2020-04-05T15:56:00.12345-08:00", "-08:00"},
+		{"2020-04-05T15:56:00.12345-08:30", "-08:30"},
+		{"2020-04-05T15:56:00.12345-08:15", "-08:15"},
+		{"2020-04-05T15:56:00.12345-08:17", ""},
+		// don't cache UTC:
+		{"2020-04-05T15:56:00.12345Z", ""},
+		{"2020-04-05T15:56:00Z", ""},
+		// too short:
+		{"123+08:00", ""},
+		{"+08:00", ""},
+	}
+	for _, tt := range tests {
+		if got := zoneOf(tt.in); got != tt.want {
+			t.Errorf("zoneOf(%q) = %q; want %q", tt.in, got, tt.want)
+		}
+	}
+}
+
+func BenchmarkGoParse3339(b *testing.B) {
+	b.ReportAllocs()
+	const in = `2020-04-05T15:56:00.148487491+08:00`
+	for i := 0; i < b.N; i++ {
+		_, err := time.Parse(time.RFC3339Nano, in)
+		if err != nil {
+			b.Fatal(err)
+		}
+	}
+}
+
+func BenchmarkGoParse3339InLocation(b *testing.B) {
+	b.ReportAllocs()
+	const in = `2020-04-05T15:56:00.148487491+08:00`
+
+	t, err := time.Parse(time.RFC3339Nano, in)
+	if err != nil {
+		b.Fatal(err)
+	}
+	loc := t.Location()
+
+	t2, err := time.ParseInLocation(time.RFC3339Nano, in, loc)
+	if err != nil {
+		b.Fatal(err)
+	}
+	if !t.Equal(t2) {
+		b.Fatal("not equal")
+	}
+	if s1, s2 := t.Format(time.RFC3339Nano), t2.Format(time.RFC3339Nano); s1 != s2 {
+		b.Fatalf("times don't stringify the same: %q vs %q", s1, s2)
+	}
+
+	for i := 0; i < b.N; i++ {
+		_, err := time.ParseInLocation(time.RFC3339Nano, in, loc)
+		if err != nil {
+			b.Fatal(err)
+		}
+	}
+}
+
+func BenchmarkParse3339(b *testing.B) {
+	b.ReportAllocs()
+	const in = `2020-04-05T15:56:00.148487491+08:00`
+
+	t, err := time.Parse(time.RFC3339Nano, in)
+	if err != nil {
+		b.Fatal(err)
+	}
+
+	t2, err := Parse3339(in)
+	if err != nil {
+		b.Fatal(err)
+	}
+	if !t.Equal(t2) {
+		b.Fatal("not equal")
+	}
+	if s1, s2 := t.Format(time.RFC3339Nano), t2.Format(time.RFC3339Nano); s1 != s2 {
+		b.Fatalf("times don't stringify the same: %q vs %q", s1, s2)
+	}
+
+	for i := 0; i < b.N; i++ {
+		_, err := Parse3339(in)
+		if err != nil {
+			b.Fatal(err)
+		}
+	}
+}