I modified the apalike.bst entry for bib.sort.order and merely swapped sort.label (which had been first) with year field.or.null sortify, to read as
FUNCTION {bib.sort.order}
{ year field.or.null sortify
" "
*
sort.label
*
" "
*
title field.or.null
sort.format.title
*
#1 entry.max$ substring$
'sort.key$ :=
}
Thus, with the following MWE,
\documentclass{article}
\usepackage{filecontents}
\begin{filecontents}{junk.bib}
@ARTICLE{bake67,
TITLE = "Prediction and scaling of reflected impulse from
strong blast waves",
AUTHOR = "Baker, W. E.",
JOURNAL = "International Journal of Mechanical Sciences",
VOLUME = "9",
NUMBER = "1",
PAGES = "45--51",
YEAR = "1967" }
@ARTICLE{Acme72,
TITLE = "Prediction and scaling of reflected impulse from
strong blast waves",
AUTHOR = "Acme, W. E.",
JOURNAL = "International Journal of Mechanical Sciences",
VOLUME = "9",
NUMBER = "1",
PAGES = "45--51",
YEAR = "1972" }
@ARTICLE{cake71,
TITLE = "Prediction and scaling of reflected impulse from
strong blast waves",
AUTHOR = "Cake, W. E.",
JOURNAL = "International Journal of Mechanical Sciences",
VOLUME = "9",
NUMBER = "1",
PAGES = "45--51",
YEAR = "1971" }
@ARTICLE{Delta71,
TITLE = "Prediction and scaling of reflected impulse from
strong blast waves",
AUTHOR = "Delta, W. E.",
JOURNAL = "International Journal of Mechanical Sciences",
VOLUME = "9",
NUMBER = "1",
PAGES = "45--51",
YEAR = "1971" }
\end{filecontents}
\begin{document}
cite \cite{bake67, Acme72, cake71, Delta71}
\bibliographystyle{apalike}
\bibliography{junk}
\end{document}
I get the following result, sorted by year and, within a year, by surname:

If you wish the reverse order (chronologically descending), then the line near the end of the apalike.bst file that reads
ITERATE {call.type$}
must be changed to
REVERSE {call.type$}
Of course, this means that, within a given year, surnames will likewise be sorted in reverse order, too (alphabetically backwards).
When using the original definition, which was
% Now that the label is right we sort for real,
% on sort.label then year then title. This is
% for the second sorting pass.
FUNCTION {bib.sort.order}
{ sort.label
" "
*
year field.or.null sortify
*
" "
*
title field.or.null
sort.format.title
*
#1 entry.max$ substring$
'sort.key$ :=
}
the result is sorted by surname as
