I've just fixed that in tex4ht-html4.tex.

This input:

\chapter*{Hello}
world

\chapter{This}
is better

produces wrong output:

<h2 class="likechapterHead"><a
id="x1-3000"></a>Hello</h2> world
pterHead"><span class="titlemark">Kapitola 1</span><br /><a
id="x1-40001"></a>This</h2>
<!--l. 36--><p class="noindent" >is better
</p>

note the missing `<p>` element after `Hello</h2>`. The configuration for `\chapter` and `\chapter*` in `tex4ht-html4.tex` differs in one thing:

\Configure{chapter}{}{}
{\IgnorePar\EndP\HCode{<h2 class="chapterHead"\a:LRdir>}%
\TitleMark{\HCode{<br />}}}
{\HCode{</h2>}\IgnoreIndent\par}

\Configure{likechapter}{}{}
{\IgnorePar\EndP\HCode{<h2 class="likechapterHead"\a:LRdir>}}
{\HCode{</h2>}\IgnoreIndent}

it is missing `\par` after `\IgnoreIndent`. Does it have some deeper meaning?

Because of huge code duplication configuration for `likechapter` contains `\par` for some document classes. Configurations for lower sectioning levels (likesection, likesubsection) contains `\par` and furthermore `\ShowPar` commands, so they doesn't show this behavior.