Equilibrium statistics of a single associating polymer chain are studi
ed by means of extensive Monte-Carlo computer simulations. The chain i
s treated as a self-avoiding random walk. Each associating group or st
icker is constrained to be adjacent to one other sticker, though stick
ers are free to change partners. In three dimensions chains with alter
nating long and short intervals between the stickers have a swollen co
nformation for almost all sticker placements, with the predominant ass
ociation occurring between chemically nearby groups. The observed swel
ling is consistent with a Flory picture with an excluded volume parame
ter that varies linearly with the placement asymmetry x, defined as th
e ratio of the short interval to the sum of the long and short interva
ls between the stickers. A scaling analysis of the simulations is used
to estimate that a chain with x = 0.496 +/- 0.004 will behave as an i
deal chain in the asymptotic limit. Since the maximum x equals 0.5, in
which case the stickers are equally spaced, collapsed behavior is onl
y possible for chains with almost equally spaced stickers. In two dime
nsions I find swollen conformations for all sticker placements. The si
ngle chain behavior is related to the solution properties of many-chai
n systems.