Let
{
X
n
;
n
⩾
0
}
\{ {X_n};\,n \geqslant 0\}
be a Harris-recurrent Markov chain on a general state space. It is shown that there is a sequence of random times
{
N
i
;
i
⩾
1
}
\{ {N_i};\,i \geqslant 1\}
such that
{
X
N
i
;
i
⩾
1
}
\{ {X_{{N_i}}};{\text { }}i \geqslant 1\}
are independent and identically distributed. This idea is used to show that
{
X
n
}
\{ {X_n}\}
is equivalent to a process having a recurrence point, and to develop a regenerative scheme which leads to simple proofs of the ergodic theorem, existence and uniqueness of stationary measures.