C.R. 100.2 says that "each player needs ... some way to clearly track life totals".
In sanctioned tournaments, players "must bring" a "physical, visible, and reliable method to maintain and record game information", including life totals (M.T.R. 1.10; for limitations with respect to electronic devices in such tournaments, see M.T.R. 2.12).
With Rivals of Ixalan, the Magic Tournament Rules have changed in a manner relevant to this question. In sanctioned tournaments under the new rules—
"[o]nce [life totals] need to be tracked, each player must indicate how he or she will keep track of these totals" (M.T.R. 2.14), and
"[a]t Competitive and Professional [rules enforcement level], methods that can easily be accidentally changed (such as dice) may not be used" (M.T.R. 2.14).
In sanctioned tournaments starting when Dominaria is released (and in Prereleases), life totals are considered status information, a new category of game information (M.T.R. 4.1). In such tournaments, status information "must be announced upon change and physically tracked by the affected player" in a manner that, in general, is "visible to both players during the match", but "[a]t Competitive and Professional [rules enforcement level], methods that can easily be accidentally changed (such as dice) may not be used" for this tracking (M.T.R. 4.1). See also Toby Elliott's policy update for Dominaria.
In sanctioned tournaments, players "must bring" a "physical, visible, and reliable method to maintain and record game information", including life totals (M.T.R. 1.10; for limitations with respect to electronic devices in such tournaments, see M.T.R. 2.12).
With Rivals of Ixalan, the Magic Tournament Rules have changed in a manner relevant to this question. In sanctioned tournaments under the new rules—- "[o]nce [life totals] need to be tracked, each player must indicate how he or she will keep track of these totals" (M.T.R. 2.14), and
- "[a]t Competitive and Professional [rules enforcement level], methods that can easily be accidentally changed (such as dice) may not be used" (M.T.R. 2.14).
EDIT (Apr. 24): See comment 5.
EDIT (Jan. 8, 2019): Correction in quote.